How Do You Find Prime Factorization?
To perform the prime factorization of a number, determine the prime numbers that, when multiplied, equal the original number. Then, make a prime factor pyramid to help you find the smallest prime numbers.

Determine the prime numbers
Write the original number at the top of your paper to begin the prime factor pyramid. Find which two numbers, when multiplied, equal the original number. Write the two numbers underneath the original number with a diagonal line going from the original number to each factor.

Find the new factors
Determine if the two factors of the original number have factors or if they are prime numbers. Prime numbers can only be divided by 1 or by themselves. For example, the numbers 2, 3, 5, and 7 are prime numbers.

Continue to factor the original factors
Find the factors of your original two factors. Make a diagonal line going from each original factor, then write the new factors of each original factor underneath. Continue the process until the remaining factors are prime numbers. If given the number 144, the first two factors would be 12 and 12. Each 12 can be factored into 6 and 2, and each 6 can be factored into 3 and 2. The prime factors of 144 are 3 x 3 x 2 x 2 x 2 x 2.