# Factors

Factor is a number which divides another number without leaving any remainder.

For Example:

The factors of 12 are 1, 2, 3, 4, 6, 12

We can write it as:

12 ÷ 1 = 12

12 ÷ 2 = 6

12 ÷ 3 = 4

12 ÷ 4 = 3

12 ÷ 6 = 2

12 ÷ 12 = 1

In the above cases we can see that it leaves no remainder.

Hence we can also write,

12 × 1 = 12 where 12 and 1 are the factors of 12

Again, 6 × 2 = 12 where 6 and 2 are the factors of 12

3 × 4 = 12 where 3 and 4 are the factors of 12

If we consider the number 51

Then 17 × 3 = 51 where 17 and 3 are the factors of 51

Again 51 ÷ 3 = 17 and 51 ÷ 17 = 3 leaving no remainder and hence 3 and 17 are the factors of 51

I: If a divisor divides the dividend completely then we can say that the divisor is a factor of the dividend.

II: Suppose two or three numbers are multiplied to get the product then the numbers multiplied are called the factors of the number.

For Example:

7 × 5 × 3 = 105

Then 7, 5, 3 are the factors of 105

Similarly 11 × 2 × 3 = 66

Then, 11, 2, and 3 are the factors of 66

III: 1 is the factor of every number because 1 multiplied by any number is the number itself. Again any number divided by 1 is the number itself.

For Example:

1 × 32 = 32

Where 1 is the factor of 32

Again 32 ÷ 1 = 32

Hence, 1 is the factor of 32

IV: In case of prime numbers we have only two factor always that is1 and the number itself.

Here are few more examples on factors:

1. Find the factors of:

(a) 32

(b) 81

(c) 128

(d) 56

(e) 343

Solution:

(a) The factors of 32 are:

1, 2, 4, 8, 16, 32

(b) The factors of 81 are:

1, 3, 9, 27, 81

(c) The factors of 128 are:

1, 2, 4, , 16, 32, 64, 128

(d) The factors of 56 are :

1, 2, 4, 7, 14, 28, 56

(e) The factors of 343 are:

1, 7, 49, 343

2. Find the factors of:

(a) 256

(b) 72

(c) 36

(d) 54

(e) 112

Solution:

(a) The factors of 256 are:

1, 2, 4, 8, 16, 21, 64, 128, 256

(b) The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 1, 24, 36, 72

(c) The factors of 36 are:

1, 2, 3, 4, 6, 9, 12, 18 36

(d) The factors of 54 are:

1, 2, 3, 6, 9, 18, 27, 54

(e) The factors of 112 are:

1, 2, 4, 7, 14, 28, 56, 112