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1. Identify the factors of 67 among the given numbers.
1, 3, 7, 9, 13, 27, 37, 67.

2. Identify the multiples of 7 among the given numbers.
34, 35, 37, 41, 42, 50, 49, 77, 56, 59.

3. Find all the numbers between 20 and 60 whose factors are 2, 3 and 5.
4. Write 't' for true and 'F' for false for the following statements:
(a) 127 is a prime number. (b) 533 is divisible by 3.

(c) 4 is a factor of 134. (d) 1210 is multiple of 10 and 11.

Factors

Let us consider a number, say 36, and divide it by all the possible numbers that divides the
number 36 exactly.

36 ÷ 1 = 36, 36 ÷ 2 = 18, 36 ÷ 3 = 12, 36 ÷ 4 = 9
36 ÷ 6 = 6, 36 ÷ 9 = 4, 36 ÷ 12 = 3, 36 ÷ 18 = 2, 36 ÷ 36 = 1
Clearly, 36 is completely divisible by 1, 2, 3, 4, 6, 9, 12, 18 and 36.

So, we can say, the numbers 1, 2, 3, 4, 6, 9, 12, 18 and 36 are all factors of 36.
Thus, a number is said to be a factor of another number, if it divides the number exactly

without leaving remainder.
The factors of a number can be found by either multiplication or division.

example 1: Find the factors of 24.
Solution: Using multiplication Using division Remember

1 × 24 = 24 24 ÷ 1 = 24 A factor of a
2 × 12 = 24 All possible 24 ÷ 2 = 12 All possible divisions number is an
combinations are
3 × 8 = 24 tried out. So, stop. 24 ÷ 3 = 8 are tried out. exact divisor of
So, stop.
4 × 6 = 24 24 ÷ 4 = 6 that number.
Factors Factors
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

example 2: Is 8 a factor of 192?
2 4
Solution: A factor of a number is an exact divisor of that number. 8 1 9 2

So, divide 192 by 8. – 1 6
Clearly, 8 is the exact divisor of 192. – 3 2
3 2
Hence, 8 is a factor of 192. 0

teacher’s Divide the class into groups. Assign each group a 3-digit number to find its factors. Practice them to be
tip systematic in writing all the factors of a given number.

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