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example 2: Find the factors of: (a) 24 (b) 36

Solution: (a) 1 × 24 = 24 (b) 1 × 36 = 36 Note
2 × 12 = 24 2 × 18 = 36 Stop the process

3 × 8 = 24 3 × 12 = 36 of multiplication
when factors start
4 × 6 = 24 4 × 9 = 36 repeating itself.
6 × 6 = 36

Thus, the factors of 24 are Thus, the factors of 36 are
1, 2, 3, 4, 6, 8, 12 and 24. 1, 2, 3, 4, 6, 9, 12, 18 and 36.

Using Division

To find the factors of a number using division, divide the number by each of the
possible counting number.

example 3: Find all the factors of 60.

Solution: We divide 60 by all possible counting numbers.
60 ÷ 1 = 60 ; 1 and 60 are factors of 60. 1 2 3 4 5 6 10 12 15 20 30 60

60 ÷ 2 = 30 ; 2 and 30 are factors of 60.

60 ÷ 3 = 20 ; 3 and 20 are factors of 60.
60 ÷ 4 = 15 ; 4 and 15 are factors of 60.
Note
60 ÷ 5 = 12 ; 5 and 12 are factors of 60. Continue the process of

60 ÷ 6 = 10 ; 6 and 10 are factors of 60. division till the quotient
All possible divisions are being tried out. is larger than divisor.

Thus, 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 are factors of 60.

example 4: Write all the factors of 30.
Solution: 30 ÷ 1 = 30 1 × 30 = 30

30 ÷ 2 = 15 or 2 × 15 = 30

30 ÷ 3 = 10 3 × 10 = 30
30 ÷ 5 = 6 5 × 6 = 30

Thus, the factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

to Find out Whether one Number is a Factor of another

We know that for a number to be a factor of another number, it must exactly divide
the larger number without leaving any remainder.

example 5: Check whether the first number is a factor of the second number.
(a) 7, 80 (b) 12, 144

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