# Prime Factorization of 65

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Prime factorization or integer factorization of a number is the determination of the set of prime intergers which multiply together to give the original integer. It is also known as prime decomposition.

**Converting to factors of 65**

We get integer factorization of 65 by finding list of prime numbers that can divide the number, together with their multiplicities.

This means prime numbers that can divide 65 without remainders. So first number to consider is 2

Getting factors is done by diving the number with numbers lower to it in value to find the one that will not leave remainder. Numbers that divide without remainders are the factors.

Prime factorizations is different from prime numbers. prime numbers are integer numbers that can be divided by itself and 1. for example 7 can be divided by itself and 1, so it is a prime number.

Integer Numbers that can be divided by other numbers are called composite numbers. Prme factorizations are done on composite numbers and not on prime numbers.

The first 10 prime integers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

** Factorization example**

Let's say we want to find the prime factors of 50. We start testing all integers to see if and how often they divide 50 and the subsequent resulting Value. The resulting set of factors will be prime since, for example, when 2 is exhausted, all multiples of 2 will also be exhausted.

50 ÷ 2 = 25; save 2

25 ÷ 2 = 12.5, not integer so try next highest number, 3

25 ÷ 3 = 8.333, not integer so try next highest number, 4

25 ÷ 4 = 6.25, not integer so try next highest number, 5

25 ÷ 5 = 5; save 5

5 ÷ 5 = 1; save 5

So 50 factors= 2 x 5 x 5 which is the same as 2 x 5^{2}

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