Page 33 - SM Class 5 Inner.cdr

“Prime Factorization” is finding which prime numbers multiply together to
make the original number. So, a factorization in which every factor is a prime
number is called prime factorization of the number.

Example 3 : What are prime factors of 15, 20 and 330. Note
Solution : The prime factors of 15 are 3 and 5 :
Prime Factorization can be checked by
15 = 3 × 5
multiplying all the factors.
The prime factors of 20 are 2, 2 and 5 :
20 = 2 × 2 × 5
The prime factors of 330 are 2, 3, 5 and 11 :
330 = 2 × 3 × 5 × 11

There are two method of writing prime factorization.

1. Division method 2. Factor tree method

1. Division Method
You take a number and check with the smallest prime number (2) if it gets
divided completely. Then you move in checking for each of the prime number
until we get 1 at the end of the ladder.

Example 4 : Find prime factors by Divsion Method : 40, 36, 126

Solution : 2 40 2 36 2 126

2 20 2 18 3 63
2 10 3 9 3 21
5 5 3 3 7 7

1 1 1
40 = 2 × 2 × 2 × 5 36 = 2 × 2 × 3 × 3 126 = 2 × 3 × 3 × 7

2. Factor Tree Method
Find any factors of the number, then the factors of those factors, and go on until
we can't factor it any more.

Example 5 : Find prime factors by factor Tree Method : 48
48
Solution : 48 = 8 × 6, so we write down ''8'' and ''6'' below 48
Now we continue and factor 8 into 4 × 2
8 6
Then 4 into 2 × 2
And lastly 6 into 3 × 2 4 2 3 2
We can't factor any more, so we have found the prime factors.

This reveals that 48 = 2 × 2 × 2 × 2 × 3 2 2

For example as for 30 we can do it in two ways.

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Mathematics In Focus - 5