Word Problem: Factors and Multiples - 3 | Mathematics for Class 5 PDF Download

Q1: Answer the Following Questions.
(a) Which is the smallest multiple of 8 greater than 60?
Ans: A multiple is the product result of one number multiplied by another number.
Here, multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80,…
Now, according to the question:
The smallest multiple of 8 greater than 60 it means 64, 72, 80, 88, 96 … which are greater than 60.
But the smallest multiple of 8 is 64.
Therefore, 64 is the smallest multiple of 8 greater than 60.

(b) What is the difference between 25th and 29th multiples of 45?
Ans: A multiple is the product result of one number multiplied by another number.
Multiples of 45: 45 , 90 , 135 , 180 , 225 , 270 , 315 , 360 , 405 , 450 , 540 , 585 , 630 , …
Now, 25th multiple of 45 = 45 × 25 = 1125
29th multiple of 45 = 45 × 29 = 1305
Now, difference = 1305 − 1125 = 180
Therefore, the answer is 180.
(c) Which is the 32nd multiple of 199 if the 31st multiple is 6169?
Ans: A multiple is the product result of one number multiplied by another number.
32nd Multiple of 199: = 199 × 32 = 6368
31st multiple of 6169: = 6169 × 31 = 1 , 91 , 239

Q2: Answer the Following Questions.
(a) Any number X is a
(i) Factor of which number?
Ans: Multiplying two whole numbers gives a product. The numbers that we multiply are the factors of the product.
A factor divides a number completely without leaving any remainder.
For example: Factor of 30 is 1 , 2 , 3 , 10 , 15 , 30

(ii) Multiple of which number?
Ans: After multiplying the number by an integer, we can get multiples. Normally the skip counting or “count by” numbers are most often called multiples.
For example: Multiples of 3: 1 × 3 = 3 , 2 × 3 = 6 , 3 × 3 = 9 , 4 × 3 = 12 , …
So, 3 , 6 , 9 , 12 , 15 , 18 , … these numbers are multiples of 3.

(b) Which is the largest 2-digit multiple of 7?
Ans: After multiplying the number by an integer, we can get multiples.
Multiples of 7: 7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 , 70 , 77 , 84 , 91 , 98 , 105 , …
Now, according to the question,
The largest 2-digit multiple of 7 = 98
Therefore, 98 is the largest 2-digit multiple of 7.

(c) Which is the smallest factor of any number?
Ans:
The factor of a number are the numbers that divide evenly into the number.
For example, the factors of the number 12 are the numbers 1, 2,3, 4,6 and 12.
Note that the smallest factor is always 1 and the largest factor is always the number itself.
Therefore, 1 is the smallest factor of any number.

Q3: Answer the Following Questions.
(a) Which is the smallest factor of any number X?
Ans: The factor of a number are the numbers that divide evenly into the number.
For example, the factors of the number 10 are the numbers 1,2, 5, and 10.
Notice that the smallest factor is always 1 and the largest factor is always the number itself.
Therefore, 1 is the smallest factor of any number X.

(b) Which is the smallest multiple of any number X?
Ans: The multiple of a number is what you get on multiplying the number with a natural number.
So, to find the smallest multiple of a number you multiply it with the smallest natural number i.e.. , 1 which result in the number itself.
Therefore, number itself is the smallest multiple of any number X.

(c) Which is the largest factor of any number X?
Ans: The factor of a number are the numbers that divide evenly into the number.
For example, the factors of the number 10 are the numbers 1,2, 5, and 10.
Notice that the smallest factor is always 1 and the largest factor is always the number itself.
Therefore, number itself is the largest factor of any number X.

(d) Which number is neither prime not composite?
Ans: A prime number has only two factors: 1 and itself.
A composite number has more than two factors.
For example: The factors of 2 are 1 × 2 . 2 is prime
The factor of 9 are 1 × 9 , 3 × 3 . 9 is composite.
So, the number 1 is neither prime nor composite.

(e) Which is the only even prime number?
Ans:
The smallest prime numbers are 2, 3, 5, 7, 11, 12,17, 19 and 23.
The number 2 is the only even number.
The number 7 has only two factors 1 and itself.
Therefore, 2 is the only even prime number.