Question

What is the prime factorization of 45?

Answer 1

`45 = 5 * 3*3`.

Explanation:

You could also write this as:

`5 *3^2`

From the multiplication table, we know that `45 = 5 * 9`.

`5` is prime, but `9` is not.

The prime factorization of `9` is `3*3`, so the prime factorization of `45` is

`45 = 5 * 3*3` --or-- `5 *3^2`.

Prime numbers are whole numbers that can only be divided by themselves and 1. The first primes are:

`2, 3, 5, 7, 11, 13, 17, 19, 23, ...`

(`2` is the ONLY even prime number. All the rest are odd.)

To arrive at a prime factorization:

1) look at the number you need to factor and decide if it can be divided by 2, 3, or 5.
2) If it can, then divide by that prime, and look at what's left.
3) Can that number be divided by 2, 3, or 5?
4) Keep going like this until you have a (multiplied) list of 2s, 3s and 5s.

If your number cannot be divided by 2, 3, or 5 , go on to the next prime, which is 7.

If the remaining factor of the original number is still not prime, go on to 11, and keep trying the known small primes in order until you end up with a factorization composed only of prime numbers.

There are many good websites about prime numbers. Try these:

https://www.mathsisfun.com/prime_numbers.html
http://mathforum.org/dr.math/faq/faq.prime.num.html

(Wikipedia's article on Prime Numbers is way complicated.)

Khan Academy has excellent videos on math topics:
https://www.khanacademy.org/math/pre-algebra/pre-algebra-factors-multiples/pre-algebra-prime-numbers/v/prime-numbers

The study of Prime numbers is part of Number Theory. Have fun with them!