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\\December 6, 2023 12:53 PM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

common Factors

The numbers which are common among the factors of two or more numbers are
called the common factors. 1 × 12 = 12 1 × 30 = 30

Let us consider any two numbers, say 12 and 30. 2 × 6 = 12 2 × 15 = 30

Factors of 12 are 1 , 2 , 3 , 4, 6 and 12. 3 × 4 = 12 3 × 10 = 30
Factors of 30 are 1 , 2 , 3 , 5, 6 10, 15 and 30. 5 × 6 = 30

Here, we can see that factors 1, 2, 3 and 6 are present in both lists of factors.

So, 1, 2, 3 and 6 are the common factors of 12 and 30.
example: Find the common factors of: (a) 8 and 10. (b) 12 and 20.

Solution: (a) The factors of 8 are 1 , 2 , 4 and 8.

The factors of 10 are 1 , 2 , 5 and 10
So, the common factors of 8 and 10 are 1 and 2.

(b) The factors of 12 are 1 , 2 , 3, 4 , 6 and 12.

The factors of 20 are 1 , 2 , 4 , 5, 10 and 20.
So, the common factors of 12 and 20 are 1, 2, and 4.

Practice time 5a

1. State whether the following statements are true or false.
(a) Every number is the factor of itself.

(b) 0 is a factor of every number.
(c) 3 is a factor of 28.

(d) The smallest factor of a number is the number itself.
2. Use multiplication method to list the factors of:

(a) 12 (b) 28 (c) 45 (d) 56 (e) 72
3. Use division method to list the factors of:
(a) 24 (b) 36 (c) 54 (d) 72 (e) 96

4. Check whether the first number is a factor of the second number.
(a) 12, 140 (b) 10, 160 (c) 8, 176 (d) 15, 220

5. Find the common factors of the following pair of numbers.
(a) 18 and 24 (b) 10 and 25 (c) 21 and 35 (d) 42 and 54

(e) 60 and 90 (f) 24 and 32 (g) 18, 24 and 32

teacher’s Discuss with the students with examples that, every number is a factor of zero. But zero is not a factor of any
tip number.

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