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example 4. Find all the factors of 30.

Solution.

using multiplication using division

1 × 30 = 30 30 ÷ 1 = 30
All possible All possible
2 × 15 = 30 combinations 30 ÷ 2 = 15 divisions are
are tried out. tried out.
3 × 10 = 30 So, stop. 30 ÷ 3 = 10 So, stop.

5 × 6 = 30 30 ÷ 5 = 6

factors factors

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

example 5. Is 8 a factor of 2468?
Solution. Let us divide 2468 by 8.
Keep in Mind
3 0 8

8 2 4 6 8
– 2 4 In case of division, if a number divides
another number without leaving a
0 6 8 remainder, then the divisor and quotient
– 6 4 both are the factors of the dividend.
0 4

The division of 2468 by 8 leaves a remainder of 4. So, 8 is not a factor of 2468.

Properties of Factors
1. 1 is a factor of every number. For example, 1 × 5 = 5, 1 × 8 = 8, 1 × 24 = 24, etc.

2. Every number is a factor of itself. For example, 7 × 1 = 7, 9 × 1 = 9, 73 × 1 = 73, etc.
3. Zero is not a factor of any number, whereas every number is a factor of zero.

4. Every non-zero number except 1 has at least two factors, while 1 has only one
factor.
5. There are a finite number of factors of a number.

For example, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. That
is, 60 has only twelve factors. So, the factors are limited.
• A number which has only two factors, that is, 1 and the number itself is called

a prime number. For example, 2, 3, 5, 7, 11, 13, 17, etc. are prime numbers.
6. The factors of a number are always less than or equal to the number itself.
For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

68 Mathematics 5