Prime Factorization - Arithmetic Step by Step

Break 60 into its prime building blocks using a division ladder. Divide by the smallest prime that works, then repeat on the quotient until you reach 1. The result: 60 = 2 × 2 × 3 × 5.

Example

prime-factorization-60.math

60

step: 60 ÷ 2 = 30
step: 30 ÷ 2 = 15
step: 15 ÷ 3 = 5
step: 5 ÷ 5 = 1
step: 60 = 2 x 2 x 3 x 5

division-ladder Start with the number and divide by the smallest prime factor. Write the quotient below and repeat. Each row shows one prime factor on the side. Stop when the quotient reaches 1. The primes on the side, read top to bottom, are the prime factorization.