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Divisibility
Prime factorization

We can break up a number into its prime numbers. This process is called prime factorization.

To write 60 in prime factored form we would get: 60 = 2 x 2 x 2 x 3 x 5.
This can be further simplified using exponents to 60 = 23 x 3 x 5.

Prime factoring is to factor and then continue factoring a number until you can no longer reduce the factors into constituent factors any further.

One way to find the prime factorization of a number is to use a factor tree such us the one shown in the following example:

 Factor 280 completely Use a factor tree like the one shown at the right. The factors are prime. List the prime factors from least to greatest: 280=2·2·2·5·7

Any number can be written as a product of prime numbers in a unique way (except for the order).

To determine the prime factors of a given number:
1. Choose the smallest prime that will divide evenly into the given number and divide.
2. Repeat step 1 on the answer until the answer is prime.

Find the prime factorization of 24:

24 can be divided by 2 (the smallest prime number). Let's check: 24 ÷ 2 = 12
But 12 is not a prime number, so we need to factor it further: 12 ÷ 2 = 6
But 6 is not a prime number, so we need to factor it further: 6 ÷ 2 = 3

And 3 is a prime number, so:

24 = 2 x 2 x 2 x 3 is the prime factorization of 24.
It can also be written as 24 = 23 x 3

Find the prime factorization of 669

 669 =