Prime Factorization

Factorization The strings of factors of a number are called factorizations of that number. The longest possible string of factors of any number is the one that is made up of all prime numbers. This is called the prime factorization of the number. Every number has its own unique prime factorization.

Factor Trees Prime factorization can be found by using a factor tree or the cake method.  Example of a factor tree:

Cake Method Example of cake method:

Using Exponents If the prime factorization of a number has more than one of the same prime number, use exponents. Remember, an exponent tells how many times a factor is used. For example, the prime factorization of 72 is 2 ● 2● 2 ● 3 ● 3. Write this as 2³ ● 3².