## FACTORS OF NUMBERS

Factors of numbers means , when a number X is divided by number Y and gives remainder 0 then we say that Y is factor of X . Lets understand this with an example.

Say we need factors of 8.

If we divide 8 by 2 we get remainder 0 and quotient as 4. Again next number 3. If we divide 8 /3 we get remainder and quotient as 2. Since we didnt get remainder 0 when divided by 3 means 3 is not factor of 8. Try with 4 we get remainder 0 and quotient as 2 . With 5,6,7 we cannot get remainder 0. Hence they cannot be factors.

*We shall remember that 1 and the number for which we need factors are always factors of the number.*

Finally if we see factors of 8 are 1, 2, 4 and 8 .

### Few things to Remember

- 1 is a factor of every number
- Any number is factor of itself.
- Minimum there are always 2 factors for every number.
- Factors are nothing but multiples of number.

#### Factors of numbers below 30

- 1 – 1
- 2 – 1 , 2
- 3 – 1 , 3
- 4 – 1, 2 , 4
- 5 – 1 , 5
- 6 – 1, 2, 3, 6
- 7 – 1, 7
- 8 – 1, 2, 4, 8
- 9 – 1, 3, 9
- 10 – 1, 2, 5,10
- 11 – 1, 11
- 12 – 1, 2, 3, 4, 6, 12
- 13 – 1, 13
- 14 – 1, 2, 7, 14
- 15 – 1 ,3, 5, 15
- 16 – 1 ,2, 4, 8, 16
- 17 – 1, 17
- 18 – 1, 2 ,3 ,6, 9,18
- 19 – 1, 19
- 20 – 1, 2, 4, 5, 10, 20
- 21 – 1, 3, 7, 21
- 22 – 1, 2, 11 , 22
- 23 – 1, 23
- 24 – 1, 2, 3, 4, 6, 8, 12, 24
- 25 – 1, 5, 25
- 26 – 1 , 2 , 13 , 26
- 27 – 1, 3, 9, 27
- 28 – 1, 2, 4, 7, 14 , 28
- 29 – 1, 29

Here if we observe for 6 and 28 Sum of factors is equal to twice the number.

For 6– Twice of 6 = 12 and sum of factors = 1 +2 +3+6 = 12

For 28 Twice of 28 = 56 and sum of factors = 1 + 2+4+7+14+28 =56

Note – If sum of factors equals to twice the number then that number is called as PERFECT NUMBER.

Here 6 and 28 are perfect numbers.