# Prime Factorization

### Prime Number:

A number which is divisible by 1 and by itself is called prime number.

### Prime Factorization:

If a given number say 24 is divided by 2 we start getting the factors has 24= 2$\times$2 $\times$2 $\times$ 3. Here 2 and 3 are prime factors. So 24 = 23 $\times$3.

Now let us learn to solve prime factorization with these below examples:

## Prime Factors of 15

15 = 5$\times$3.
Step 1: Divide 15 by 3
Step 2: we get 5
so prime factors are illustrated below

## Prime Factors of 28

28 = 2$\times$2$\times$7.
Step 1: Divide 28 by 2
Step 2: we get 14
Step 3: further divide by 2
Step 4: we get 7
so prime factors are illustrated below

## Prime Factors of 34

34 = 2$\times$ 17
Step 1: Divide 34 by 2
Step 2: we get 17
so prime factors are illustrated below

## Prime Factorisation of 44

44 = 2$\times$2$\times$11
Step 1: Divide 44 by 2
Step 2: we get 22
Step 3: further divide by 2
Step 4: we get 11
so prime factors are illustrated below

## Prime Factorisation of 48

48 = 2$\times$2$\times$2$\times$2$\times$3
44 = 2$\times$2$\times$11
Step 1: Divide 48 by 2
Step 2: we get 24
Step 3: further divide by 2
Step 4: we get 12
Step 5: further divide by 2
Step 6: we get 6
Step 7: further divide by 2
Step 8: we get 3
so prime factors are illustrated below

## Prime Factorisation of 56

56= 2$\times$2$\times$2$\times$7
Step 1: Divide 56 by 2
Step 2: we get 28
Step 3: further divide by2
Step 4: we get 14
Step 5: further divide by 2
Step 6: we get 7
so prime factors are illustrated below

## Prime Factorisation of 63

63= 3$\times$3$\times$9
Step 1: Divide 63 by 3
Step 2: we get 21
Step 3: further divide by 3
Step 4: we get 7
so prime factors are illustrated below

## Prime Factorisation of 72

72= 2$\times$2$\times$2$\times$3$\times$3
Step 1: Divide 72 by 2
Step 2: we get 36
Step 3: further divide by 2
Step 4: we get 18
Step 5: further divide by 2
Step 6: we get 9
Step 7: divide it by 3
Step 8: we get 3
so prime factors are illustrated below

## Prime factorisation of 75

75= 5$\times$5$\times$3
Step 1: Divide 75 by 5
Step 2: we get 15
Step 3: further divide by 5
Step 4: we get 3
Step 5: further divide by 3
Step 6: we get 1
so prime factors are illustrated below

## Prime Factorisation of 99

99 = 3$\times$3$\times$ 11
Step 1: Divide 99 by 3
Step 2: we get 33
Step 3: further divide by3
Step 4: we get 11
Step 5: further divide by 11
Step 6: we get 1
so prime factors are illustrated below

## Prime factorisation of 100

100 = 2$\times$2$\times$5$\times$5
Step 1: Divide 100 by 5
Step 2: we get 20
Step 3: further divide by 5
Step 4: we get 4
Step 5: further divide by 2
Step 6: we get 2
Step 7: further divide by 2
Step 8: we get 1.
so prime factors are illustrated below

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