Class 5 Maths - Be My Multiple I will be Your Factor - CBSE Worksheets Solutions - 1

Q1. Fill in the blanks with the next two numbers in the pattern: 

 (i) 2, 4, 8, 16, ____, ____.
 (ii) 3, 6, 9, ____, ____.

 (iii) 1, 3, 5, ____, ____.

 (iv) 10, 20, 30, ____, ____.

Ans:  

(i) Next two numbers are 2, 4, 8, 16, 32, 64.

The sequence is doubling at each step:

• 2$\mathrm{<span\; style="font-size:\; 20px;\; background-color:\; transparent;\; font-family:\; Lato,\; sans-serif;\; letter-spacing:\; inherit;\; word-break:\; break-word;\; line-height:\; 1.8;">\times </span>}$2=4$2\; \backslash times\; 2\; =\; 4$
• 4×2=8
• 8×2=16$8\; \backslash times\; 2\; =\; 16$

Following the same pattern:

• 16×2=32
• 32×2=64$32\; \backslash times\; 2\; =\; 64$

Thus, the next two terms in the sequence are 32 and 64.

(ii) Next two numbers are 3, 6, 9, 12, 15.  

The sequence increases by 3 at each step:

• 3+3=6
• 6+3=9$6\; +\; 3\; =\; 9$

Following the same pattern:

• 9+3=12
• 12+3=15$12\; +\; 3\; =\; 15$

Thus, the next two terms in the sequence are 12 and 15.

(iii) Next two numbers are 1, 3, 5, 7, 9. 

The sequence increases by 2 at each step:

• 1+2=3
• 3+2=5$3\; +\; 2\; =\; 5$

Following the same pattern:

• 5+2=7
• 7+2=9$7\; +\; 2\; =\; 9$

Thus, the next two terms in the sequence are 7 and 9.

(iv) Next two numbers are 10, 20, 30, 40, 50.

The sequence increases by 10 at each step:

• 10+10=20
• 20+10=30$20\; +\; 10\; =\; 30$

Following the same pattern:

• 30+10=40
• 40+10=50$40\; +\; 10\; =\; 50$

Thus, the next two terms in the sequence are 40 and 50.

Q2. Word Problems:

 (i) If you start counting by 3s starting from 0, what is the 7th number you will say?

Ans: The 7th number will be 18. 

When you count by 3s starting from 0, you're repeatedly adding 3 to each number. Here's the process for each step:

1. Start at 0.
2. Add 3 to get the next number: $0+3=3.$
3. Add 3 again: $3+3=6.3\; +\; 3\; =\; 6$
4. Keep adding 3 for each step after that:

0,3,6,9,12,15,18, ....

Now, let's count these steps:

The 1st number is 0.

The 2nd number is 3.

The 3rd number is 6.

The 4th number is 9.

The 5th number is 12.

The 6th number is 15.

The 7th number is 18.

So, the 7th number when counting by 3s starting from 0 is 18.

 (ii) Maria collects stickers. She has 5 stickers and collects 5 more each week. Write the pattern of how many stickers she will have at the  end of each week for 5 weeks.

Ans:  The pattern is as follows:

Week 1: 10 stickers

Week 2: 15 stickers

Week 3: 20 stickers

Week 4: 25 stickers

Week 5: 30 stickers

Week 1: Maria starts with 5 stickers and collects 5 more, so:
5+5=10$5\; +\; 5\; =\; 10$ stickers.

Week 2: She collects another 5 stickers:
10+5=15$10\; +\; 5\; =\; 15$ stickers.

Week 3: She collects another 5 stickers:
15+5=20$15\; +\; 5\; =\; 20$ stickers.

Week 4: She collects another 5 stickers:
20+5=25$20\; +\; 5\; =\; 25$ stickers.

Week 5: She collects another 5 stickers:
25+5=30$25\; +\; 5\; =\; 30$ stickers.

 (iii) James is planting trees in rows. He plants 4 trees in each row. If he plants 5 rows, how many trees does he plant in total? Write the  pattern of the total number of trees after each row.

Ans: The pattern is as follows:

After Row 1: 4 trees

After Row 2: 8 trees

After Row 3: 12 trees

After Row 4: 16 trees

After Row 5: 20 trees

Row 1:
4×1=4 trees planted.

Row 2:
4×2=8 trees planted.

Row 3:
4×3=12 trees planted.

Row 4:
4×4=16$4\; \backslash times\; 4\; =\; 16$ trees planted.

Row 5:
4×5=20 trees planted.

Q3: Practice the questions given in the worksheet on factors and multiples.

(i) Find out the even numbers.
27, 36, 48, 125, 360, 453, 518, 423, 54, 58, 917, 186, 423, 928, 358
Ans: 36, 48, 360, 518, 54, 58, 186, 928, 358

To find the even numbers in the list, we need to identify the numbers that are divisible by 2.

(ii) Find out the odd numbers.
10, 45, 78, 146, 347, 543, 495, 638, 497, 968, 729, 427, 624, 572
Ans: 45, 347, 543, 495, 497, 729, 427

To find the odd numbers in the list, we need to identify the numbers that are not divisible by 2.

(iii) Write the factors of the following:
(a) 27
(b) 32
(c) 18
(d) 45
(e) 25
(f) 56
(g) 68
(h) 38
(i) 72
(j) 56
Ans: Factors are the numbers that can divide a number exactly. 
(a)  Factors are 1, 3, 9, 27

To find the factors of $2727$, we look for all the numbers that can divide $\mathrm{27 }27$without leaving a remainder. 

The factors of $2727$ are:

1 (since 27÷1=27$27\; \backslash div\; 1\; =\; 27$)

3 (since 27÷3=9$27\; \backslash div\; 3\; =\; 9$)

9 (since 27÷9=3$27\; \backslash div\; 9\; =\; 3$)

27 (since 27÷27=1$27\; \backslash div\; 27\; =\; 1$)

Factors of 27:

1, 3, 9, 27

(b)  Factors are 1, 2, 4, 8, 16, 32

To find the factors of 32, we look for all the whole numbers that can divide 32 without leaving a remainder.

Factors of 32:

1 (since $32÷1=3232\; \backslash div\; 1\; =\; 32$)

2 (since $32÷2=1632\; \backslash div\; 2\; =\; 16$)

4 (since $32÷4=832\; \backslash div\; 4\; =\; 8$)

8 (since $32÷8=432\; \backslash div\; 8\; =\; 4$)

16 (since $32÷16=232\; \backslash div\; 16\; =\; 2$)

32 (since $32÷32=132\; \backslash div\; 32\; =\; 1$)

The factors of 32 are: 1, 2, 4, 8, 16, 32.

(c) Factors are 1, 2, 3, 6, 9, 18

Now, solve the remaining parts by referring to the above two examples.

(d)  Factors are 1, 3, 5, 9, 15, 45
(e)  Factors are 1, 5, 25
(f)  Factors are 1, 2, 4, 7, 8, 14, 28, 56
(g)  Factors are 1, 2, 4, 17, 34, 68
(h)  Factors are 1, 2, 19, 38
(i)  Factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
(j)  Factors are 1, 2, 4, 7, 8, 14, 28, 56

(iv) Write the first five multiples of the following:
(a) 4
(b) 3
(c) 7
(d) 9
(e) 5
(f) 8
(g) 12
(h) 15
Ans: 

The first five multiples of a number are obtained by multiplying that number by the integers 1 to 5. Here’s a general formula:

• First multiple: $n\times 1n\; \backslash times\; 1$
• Second multiple: $n\times 2n\; \backslash times\; 2$
• Third multiple: $n\times 3n\; \backslash times\; 3$
• Fourth multiple: $n\times 4n\; \backslash times\; 4$
• Fifth multiple: $n\times 5n\; \backslash times\; 5$

(a)  First five mutiples of 4 are 4, 8, 12, 16, 20.

The first five multiples of 4 can be found by multiplying 4 by the integers $11$ to $5$:

1. $\mathrm{ 4}\times 1=44\; \backslash times\; 1\; =\; 4$
2. $\mathrm{ 4}\times 2=84\; \backslash times\; 2\; =\; 8$
3. $\mathrm{ 4}\times 3=124\; \backslash times\; 3\; =\; 12$
4. $\mathrm{ 4}\times 4=164\; \backslash times\; 4\; =\; 16$
5. $\mathrm{ 4}\times 5=204\; \backslash times\; 5\; =\; 20$

First five multiples of 4 :  4, 8, 12, 16, 20.

(b) First five mutiples of 3 are 3, 6, 9, 12, 15

For 3:

• 3×1=3
• 3×2=6
• 3×3=9
• 3×4=12
• 3×5=15

First five multiples of 3: 3, 6, 9, 12, 15

(c) First five multiples of 7 are 7, 14, 21, 28, 35

Now, using the above method, the rest can be found out.

(d) First five mutiples of 9 are 9, 18, 27, 36, 45
(e) First five mutiples of 5 are 5, 10, 15, 20, 25
(f) First five mutiples of 8 are 8, 16, 24, 32, 40
(g) First five mutiples of 12 are 12, 24, 36, 48, 60
(h) First five mutiples of 15 are  15, 30, 45, 60, 75

(v) Find the first three multiples of 8.
Ans: 8, 16, 24

(vi) Find the missing factors.
(a) 7 × ___ = 56
(b) 5 × ___ = 30
(c) ___ × 3 = 24
(d) 6 × ___ = 48
(e) 8 × ___ = 72
Ans:
(a) 7 × 8 = 56

To find the missing factor in the equation $7\times \_\_=567\; \backslash times\; \backslash \_\backslash \_\; =\; 5$, you can divide $5656$ by $\mathrm{<br\; style="word-break:\; break-word;\; line-height:\; 1.8;\; font-family:\; Lato,\; sans-serif;\; font-size:\; 20px;\; letter-spacing:\; inherit;\; color:\; black;">}7$7.

Now, calculate it: 

How many times does $77$ fit into $5656$?

If you count by $\mathrm{7:}$

$7,14,21,28,35,42,49,56$

You find that $77$ goes into $5656$ exactly 8 times.

So, the missing factor is 8. 

(b) 5 × 6 = 30 

The rest can be solved with reference to the first one.

(c)  8 × 3 = 24

(d) 6 × 8 = 48

(e) 8 × 9 = 72

(vii) Write the multiples of 6 which are greater than 20 and less than 50.
Ans: 24, 30, 36, 42, 48

List the multiples of 6:

6×1=6$6\; \backslash times\; 1\; =\; 6$

6×2=12$6\; \backslash times\; 2\; =\; 12$

6×3=18$6\; \backslash times\; 3\; =\; 18$

6×4=24

6×5=30

6×6=36

6×7=42

6×8=48

6×9=54

Select the multiples that are greater than 20 and less than 50:

24 (greater than 20 and less than 50)

30 (greater than 20 and less than 50)

36 (greater than 20 and less than 50)

42 (greater than 20 and less than 50)

48 (greater than 20 and less than 50)

So, The multiples of 6 that are greater than 20 and less than 50 are:24, 30, 36, 42, 48.