NCERT Textbook: Prime Time | Mathematics (Maths) Class 6 PDF Download

 Page 1


Children sit in a circle and play a game of numbers.
One of the children starts by saying ‘1’. The second 
player says ‘2’, and so on. But when it is the turn of 3, 6, 
9, … (multiples of 3), the player should say ‘idli’ instead 
of the number. When it is the turn of 5, 10, … (multiples 
of 5), the player should say ‘vada’ instead of the number. 
When a number is both a multiple of 3 and a multiple 
of 5, the player should say ‘idli-vada’! If a player makes 
any mistake, they are out.
The game continues in rounds till only one person 
remains.
For which numbers should the players say ‘idli’ 
instead of saying the number? These would be 3, 6, 9, 
12, 18, … and so on.
For which numbers should the players say ‘vada’? 
These would be 5, 10, 20, … and so on.
Which is the first number for which the players 
should say, ‘idli-vada’? It is 15, which is a multiple of 3, 
and also a multiple of 5. Find out other such numbers 
that are multiples of both 3 and 5. These numbers are 
called _____________________________.
Idli-Vada Game
PRIME TIME
5
5.1 Common Multiples and Common Factors
Chapter 5_Prime Time.indd   107 09-08-2024   16:59:59
Page 2


Children sit in a circle and play a game of numbers.
One of the children starts by saying ‘1’. The second 
player says ‘2’, and so on. But when it is the turn of 3, 6, 
9, … (multiples of 3), the player should say ‘idli’ instead 
of the number. When it is the turn of 5, 10, … (multiples 
of 5), the player should say ‘vada’ instead of the number. 
When a number is both a multiple of 3 and a multiple 
of 5, the player should say ‘idli-vada’! If a player makes 
any mistake, they are out.
The game continues in rounds till only one person 
remains.
For which numbers should the players say ‘idli’ 
instead of saying the number? These would be 3, 6, 9, 
12, 18, … and so on.
For which numbers should the players say ‘vada’? 
These would be 5, 10, 20, … and so on.
Which is the first number for which the players 
should say, ‘idli-vada’? It is 15, which is a multiple of 3, 
and also a multiple of 5. Find out other such numbers 
that are multiples of both 3 and 5. These numbers are 
called _____________________________.
Idli-Vada Game
PRIME TIME
5
5.1 Common Multiples and Common Factors
Chapter 5_Prime Time.indd   107 09-08-2024   16:59:59
Ganita Prakash | Grade 6
108
 Figure it Out
1. At what number is ‘idli-vada’ said for the 10
th
 time?
2. If the game is played for the numbers from 1 till 90, find out:
a. How many times would the children say ‘idli’ (including the 
times they say ‘idli-vada’)?
b. How many times would the children say ‘vada’ (including the 
times they say ‘idli-vada’)?
c. How many times would the children say ‘idli-vada’?
3. What if the game was played till 
900? How would your answers 
change?
4.  Is this figure somehow related to 
the ‘idli-vada’ game?
Hint:  Imagine playing the game 
till 30. Draw the figure if 
the game is played till 60.
 Let us now play the ‘idli-vada’ game 
with different pairs of numbers: 
a. 2 and 5, 
b. 3 and 7, 
c. 4 and 6. 
We will say ‘idli’ for multiples of the smaller number, ‘vada’ for 
multiples of the larger number and ‘idli-vada’ for common multiples. 
Draw a figure similar to Fig. 5.1 if the game is played up to 60.
Y esterday we played this game  
with two numbers. We ended  
up saying just ‘idli’ or ‘idli-vada’ 
and nobody said just ‘vada’!
Oh, what could  
those numbers be!? 
One of the numbers 
was 4.
Fig. 5.1
Multiples 
of 3
Multiples 
of 5
21
21
30
15
10
20
5
25
12
18
27
9
3
Common multiples 
of 3 and 5
Chapter 5_Prime Time.indd   108 09-08-2024   17:00:00
Page 3


Children sit in a circle and play a game of numbers.
One of the children starts by saying ‘1’. The second 
player says ‘2’, and so on. But when it is the turn of 3, 6, 
9, … (multiples of 3), the player should say ‘idli’ instead 
of the number. When it is the turn of 5, 10, … (multiples 
of 5), the player should say ‘vada’ instead of the number. 
When a number is both a multiple of 3 and a multiple 
of 5, the player should say ‘idli-vada’! If a player makes 
any mistake, they are out.
The game continues in rounds till only one person 
remains.
For which numbers should the players say ‘idli’ 
instead of saying the number? These would be 3, 6, 9, 
12, 18, … and so on.
For which numbers should the players say ‘vada’? 
These would be 5, 10, 20, … and so on.
Which is the first number for which the players 
should say, ‘idli-vada’? It is 15, which is a multiple of 3, 
and also a multiple of 5. Find out other such numbers 
that are multiples of both 3 and 5. These numbers are 
called _____________________________.
Idli-Vada Game
PRIME TIME
5
5.1 Common Multiples and Common Factors
Chapter 5_Prime Time.indd   107 09-08-2024   16:59:59
Ganita Prakash | Grade 6
108
 Figure it Out
1. At what number is ‘idli-vada’ said for the 10
th
 time?
2. If the game is played for the numbers from 1 till 90, find out:
a. How many times would the children say ‘idli’ (including the 
times they say ‘idli-vada’)?
b. How many times would the children say ‘vada’ (including the 
times they say ‘idli-vada’)?
c. How many times would the children say ‘idli-vada’?
3. What if the game was played till 
900? How would your answers 
change?
4.  Is this figure somehow related to 
the ‘idli-vada’ game?
Hint:  Imagine playing the game 
till 30. Draw the figure if 
the game is played till 60.
 Let us now play the ‘idli-vada’ game 
with different pairs of numbers: 
a. 2 and 5, 
b. 3 and 7, 
c. 4 and 6. 
We will say ‘idli’ for multiples of the smaller number, ‘vada’ for 
multiples of the larger number and ‘idli-vada’ for common multiples. 
Draw a figure similar to Fig. 5.1 if the game is played up to 60.
Y esterday we played this game  
with two numbers. We ended  
up saying just ‘idli’ or ‘idli-vada’ 
and nobody said just ‘vada’!
Oh, what could  
those numbers be!? 
One of the numbers 
was 4.
Fig. 5.1
Multiples 
of 3
Multiples 
of 5
21
21
30
15
10
20
5
25
12
18
27
9
3
Common multiples 
of 3 and 5
Chapter 5_Prime Time.indd   108 09-08-2024   17:00:00
Prime Time 
109
  Which of the following could be the other number:
 2, 3, 5, 8, 10?
Jump Jackpot
Jumpy and Grumpy play a game.
•  Grumpy places a treasure on some number. For example, he 
may place it on 24.
•  Jumpy chooses a jump size. If he chooses 4, then he has to 
jump only on multiples of 4, starting at 0.
•  Jumpy gets the treasure if he lands on the number where 
Grumpy placed it.
Which jump sizes will get Jumpy to land on 24?
If he chooses 4: Jumpy lands on 4 ? 8 ? 12 ? 16 ? 20 ? 24 ? 28 ? ...
Other successful jump sizes are 2, 3, 6, 8 and 12.
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
What about jump sizes 1 and 24? Yes, they also will land on 24.
The numbers 1, 2, 3, 4, 6, 8, 12, 24 all divide 24 exactly. Recall that 
such numbers are called factors or divisors of 24.
Grumpy increases the level of the game. Two treasures are kept 
on two different numbers. Jumpy has to choose a jump size and stick 
to it. Jumpy gets the treasures only if he lands on both the numbers 
with the chosen jump size. As before, Jumpy starts at 0.
Grumpy has kept the treasures on 14 and 36. Jumpy chooses a 
jump size of 7.
Will Jumpy land on both the treasures? Starting from 0, he jumps 
to 7 ? 14 ? 21 ? 28 ? 35 ? 42 … We see that he landed on 14 but 
Chapter 5_Prime Time.indd   109 09-08-2024   17:00:00
Page 4


Children sit in a circle and play a game of numbers.
One of the children starts by saying ‘1’. The second 
player says ‘2’, and so on. But when it is the turn of 3, 6, 
9, … (multiples of 3), the player should say ‘idli’ instead 
of the number. When it is the turn of 5, 10, … (multiples 
of 5), the player should say ‘vada’ instead of the number. 
When a number is both a multiple of 3 and a multiple 
of 5, the player should say ‘idli-vada’! If a player makes 
any mistake, they are out.
The game continues in rounds till only one person 
remains.
For which numbers should the players say ‘idli’ 
instead of saying the number? These would be 3, 6, 9, 
12, 18, … and so on.
For which numbers should the players say ‘vada’? 
These would be 5, 10, 20, … and so on.
Which is the first number for which the players 
should say, ‘idli-vada’? It is 15, which is a multiple of 3, 
and also a multiple of 5. Find out other such numbers 
that are multiples of both 3 and 5. These numbers are 
called _____________________________.
Idli-Vada Game
PRIME TIME
5
5.1 Common Multiples and Common Factors
Chapter 5_Prime Time.indd   107 09-08-2024   16:59:59
Ganita Prakash | Grade 6
108
 Figure it Out
1. At what number is ‘idli-vada’ said for the 10
th
 time?
2. If the game is played for the numbers from 1 till 90, find out:
a. How many times would the children say ‘idli’ (including the 
times they say ‘idli-vada’)?
b. How many times would the children say ‘vada’ (including the 
times they say ‘idli-vada’)?
c. How many times would the children say ‘idli-vada’?
3. What if the game was played till 
900? How would your answers 
change?
4.  Is this figure somehow related to 
the ‘idli-vada’ game?
Hint:  Imagine playing the game 
till 30. Draw the figure if 
the game is played till 60.
 Let us now play the ‘idli-vada’ game 
with different pairs of numbers: 
a. 2 and 5, 
b. 3 and 7, 
c. 4 and 6. 
We will say ‘idli’ for multiples of the smaller number, ‘vada’ for 
multiples of the larger number and ‘idli-vada’ for common multiples. 
Draw a figure similar to Fig. 5.1 if the game is played up to 60.
Y esterday we played this game  
with two numbers. We ended  
up saying just ‘idli’ or ‘idli-vada’ 
and nobody said just ‘vada’!
Oh, what could  
those numbers be!? 
One of the numbers 
was 4.
Fig. 5.1
Multiples 
of 3
Multiples 
of 5
21
21
30
15
10
20
5
25
12
18
27
9
3
Common multiples 
of 3 and 5
Chapter 5_Prime Time.indd   108 09-08-2024   17:00:00
Prime Time 
109
  Which of the following could be the other number:
 2, 3, 5, 8, 10?
Jump Jackpot
Jumpy and Grumpy play a game.
•  Grumpy places a treasure on some number. For example, he 
may place it on 24.
•  Jumpy chooses a jump size. If he chooses 4, then he has to 
jump only on multiples of 4, starting at 0.
•  Jumpy gets the treasure if he lands on the number where 
Grumpy placed it.
Which jump sizes will get Jumpy to land on 24?
If he chooses 4: Jumpy lands on 4 ? 8 ? 12 ? 16 ? 20 ? 24 ? 28 ? ...
Other successful jump sizes are 2, 3, 6, 8 and 12.
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
What about jump sizes 1 and 24? Yes, they also will land on 24.
The numbers 1, 2, 3, 4, 6, 8, 12, 24 all divide 24 exactly. Recall that 
such numbers are called factors or divisors of 24.
Grumpy increases the level of the game. Two treasures are kept 
on two different numbers. Jumpy has to choose a jump size and stick 
to it. Jumpy gets the treasures only if he lands on both the numbers 
with the chosen jump size. As before, Jumpy starts at 0.
Grumpy has kept the treasures on 14 and 36. Jumpy chooses a 
jump size of 7.
Will Jumpy land on both the treasures? Starting from 0, he jumps 
to 7 ? 14 ? 21 ? 28 ? 35 ? 42 … We see that he landed on 14 but 
Chapter 5_Prime Time.indd   109 09-08-2024   17:00:00
Ganita Prakash | Grade 6
110
did not land on 36, so he does not get the treasure. What jump size 
should he have chosen?
The factors of 14 are: 1, 2, 7, 14. So these jump sizes will la nd on 14.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36. These jump sizes 
will land on 36.
So, the jump sizes of 1 or 2 will land on both 14 and 36. Notice that 
1 and 2 are the common factors of 14 and 36.
The jump sizes using which both the treasures can be reached are 
the common factors of the two numbers where the treasures are 
placed.
  What jump size can reach both 15 and 30? There are multiple 
jump sizes possible. Try to find them all.
 Look at the table below. What do you notice?
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
In the table,
1. Is there anything common among the shaded 
numbers?
2. Is there anything common among the circled 
numbers?
3. Which numbers are both shaded and circled? What 
are these numbers called?
 Figure it Out
 1.  Find all multiples of 40 that lie between 310 and 410.
Math 
Talk
Chapter 5_Prime Time.indd   110 09-08-2024   17:00:00
Page 5


Children sit in a circle and play a game of numbers.
One of the children starts by saying ‘1’. The second 
player says ‘2’, and so on. But when it is the turn of 3, 6, 
9, … (multiples of 3), the player should say ‘idli’ instead 
of the number. When it is the turn of 5, 10, … (multiples 
of 5), the player should say ‘vada’ instead of the number. 
When a number is both a multiple of 3 and a multiple 
of 5, the player should say ‘idli-vada’! If a player makes 
any mistake, they are out.
The game continues in rounds till only one person 
remains.
For which numbers should the players say ‘idli’ 
instead of saying the number? These would be 3, 6, 9, 
12, 18, … and so on.
For which numbers should the players say ‘vada’? 
These would be 5, 10, 20, … and so on.
Which is the first number for which the players 
should say, ‘idli-vada’? It is 15, which is a multiple of 3, 
and also a multiple of 5. Find out other such numbers 
that are multiples of both 3 and 5. These numbers are 
called _____________________________.
Idli-Vada Game
PRIME TIME
5
5.1 Common Multiples and Common Factors
Chapter 5_Prime Time.indd   107 09-08-2024   16:59:59
Ganita Prakash | Grade 6
108
 Figure it Out
1. At what number is ‘idli-vada’ said for the 10
th
 time?
2. If the game is played for the numbers from 1 till 90, find out:
a. How many times would the children say ‘idli’ (including the 
times they say ‘idli-vada’)?
b. How many times would the children say ‘vada’ (including the 
times they say ‘idli-vada’)?
c. How many times would the children say ‘idli-vada’?
3. What if the game was played till 
900? How would your answers 
change?
4.  Is this figure somehow related to 
the ‘idli-vada’ game?
Hint:  Imagine playing the game 
till 30. Draw the figure if 
the game is played till 60.
 Let us now play the ‘idli-vada’ game 
with different pairs of numbers: 
a. 2 and 5, 
b. 3 and 7, 
c. 4 and 6. 
We will say ‘idli’ for multiples of the smaller number, ‘vada’ for 
multiples of the larger number and ‘idli-vada’ for common multiples. 
Draw a figure similar to Fig. 5.1 if the game is played up to 60.
Y esterday we played this game  
with two numbers. We ended  
up saying just ‘idli’ or ‘idli-vada’ 
and nobody said just ‘vada’!
Oh, what could  
those numbers be!? 
One of the numbers 
was 4.
Fig. 5.1
Multiples 
of 3
Multiples 
of 5
21
21
30
15
10
20
5
25
12
18
27
9
3
Common multiples 
of 3 and 5
Chapter 5_Prime Time.indd   108 09-08-2024   17:00:00
Prime Time 
109
  Which of the following could be the other number:
 2, 3, 5, 8, 10?
Jump Jackpot
Jumpy and Grumpy play a game.
•  Grumpy places a treasure on some number. For example, he 
may place it on 24.
•  Jumpy chooses a jump size. If he chooses 4, then he has to 
jump only on multiples of 4, starting at 0.
•  Jumpy gets the treasure if he lands on the number where 
Grumpy placed it.
Which jump sizes will get Jumpy to land on 24?
If he chooses 4: Jumpy lands on 4 ? 8 ? 12 ? 16 ? 20 ? 24 ? 28 ? ...
Other successful jump sizes are 2, 3, 6, 8 and 12.
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
What about jump sizes 1 and 24? Yes, they also will land on 24.
The numbers 1, 2, 3, 4, 6, 8, 12, 24 all divide 24 exactly. Recall that 
such numbers are called factors or divisors of 24.
Grumpy increases the level of the game. Two treasures are kept 
on two different numbers. Jumpy has to choose a jump size and stick 
to it. Jumpy gets the treasures only if he lands on both the numbers 
with the chosen jump size. As before, Jumpy starts at 0.
Grumpy has kept the treasures on 14 and 36. Jumpy chooses a 
jump size of 7.
Will Jumpy land on both the treasures? Starting from 0, he jumps 
to 7 ? 14 ? 21 ? 28 ? 35 ? 42 … We see that he landed on 14 but 
Chapter 5_Prime Time.indd   109 09-08-2024   17:00:00
Ganita Prakash | Grade 6
110
did not land on 36, so he does not get the treasure. What jump size 
should he have chosen?
The factors of 14 are: 1, 2, 7, 14. So these jump sizes will la nd on 14.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18 and 36. These jump sizes 
will land on 36.
So, the jump sizes of 1 or 2 will land on both 14 and 36. Notice that 
1 and 2 are the common factors of 14 and 36.
The jump sizes using which both the treasures can be reached are 
the common factors of the two numbers where the treasures are 
placed.
  What jump size can reach both 15 and 30? There are multiple 
jump sizes possible. Try to find them all.
 Look at the table below. What do you notice?
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
In the table,
1. Is there anything common among the shaded 
numbers?
2. Is there anything common among the circled 
numbers?
3. Which numbers are both shaded and circled? What 
are these numbers called?
 Figure it Out
 1.  Find all multiples of 40 that lie between 310 and 410.
Math 
Talk
Chapter 5_Prime Time.indd   110 09-08-2024   17:00:00
Prime Time 
111
 2.  Who am I?
a.  I am a number less than 40. One of my factors is 7. 
 The sum of my digits is 8.
b.  I am a number less than 100. Two of my factors are 3 and 5. 
One of my digits is 1 more than the other.
3.  A number for which the sum of all its factors is equal to twice the 
number is called a perfect number. The number 28 is a perfect 
number. Its factors are 1, 2, 4, 7, 14 and 28. Their sum is 56 which 
is twice 28. Find a perfect number between 1 and 10.
4.  Find the common factors of:
a. 20 and 28  b. 35 and 50 
c. 4, 8 and 12  d. 5, 15 and 25
5.  Find any three numbers that are multiples of 25 but not multiples 
of 50.
6.  Anshu and his friends play the ‘idli-vada’ game with two numbers, 
which are both smaller than 10. The first time anybody says ‘idli-
vada’ is after the number 50. What could the two numbers be 
which are assigned ‘idli’ and ‘vada’?
7.  In the treasure hunting game, Grumpy has kept treasures on 28 
and 70. What jump sizes will land on both the numbers?
8.  In the diagram below, Guna has erased all the numbers except 
the common multiples. Find out what those numbers could be 
and fill in the missing numbers in the empty regions.
 
Multiples of ____
Common multiples
72
48
24
Multiples of ____
9. Find the smallest number that is a multiple of all the numbers 
from 1 to 10 except for 7.
10. Find the smallest number that is a multiple of all the numbers 
from 1 to 10.
Math 
Talk
Try
This
Chapter 5_Prime Time.indd   111 09-08-2024   17:00:00