## Factors of 105 –

We have to find the factors of number 105. Factors are the numbers which when divided by number 105we get the factors.

When we make pair of factors the multiplication of pair of factors gives the given number.

### Steps to find Factors of 105:

1) Firstly we divide given number 105to get remainder 0.

2) After getting answers all numbers we get are called Factors of given number.

3) 1 is the only number having factor of all numbers.

4) The given number itself is the highest factor of given number.

We find factors of 105:

Here,

We get factors of 105 are1, 3, 5, 7, 15, 21, 35 and 105.

We know,

A number which has more than two factors is called composite number.

A number 105has more than two factors.

Hence, 105 is composite number.

Also

We know,

A number which is not divided by any other number is called prime number.

In factors of 105 we get 3,5 & 7 are the prime number.

Now we find prime factorization of 105 by using LCM.

Prime factors of 105 = 3×5×7

Prime factors of 105 = 3×5×7

There are 8 factors of 105-1, 3, 5, 7, 15, 21, 35 and 105.

When we make pairs of factors the multiplication of that two factors is the given number itself.

Pairs of factors of 105: 1 × 105 = 105.

3 × 35 = 105

5 × 21 = 105

7×15 = 105

Pairs of factors of 105= (1, 105), (3, 35), (5, 21) and (7, 15).

We know Multiplication Property,

a x b = b x a

I.e. Pairs of factors of 105:(1, 105), (3, 35), (5, 21) and (7, 15).

All factors of 105 =

- Prime factor of 105= 2×3×7
- Sum of all factors of 105 =1+ 3+ 5+ 7+ 15+ 21+ 35 + 105.=192
- Pairs of factors of 105:(1, 3, 5, 7, 15, 21, 35 and 105)is same.