Factors and Multiples

Prime Factorization

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

Factor 60 with a repeated-division ladder.

highlighted = computed this step

Step 1 — Set up

Set up the numbers to test.

6060
Start a division ladder for 60.numberdivide bynext????????????factor chipsnone collected yetfinal productwait until the ladder reaches 1check: 2 x 2 x 3 x 5 = 60

Step 2 — Divide by 2

Divide by the next prime: 60 ÷ 2 = 30.

60÷2=3060 \div \hl{2} = 30
60 ÷ 2 = 30; collect 2.numberdivide bynext60230?????????factor chips2final productwait until the ladder reaches 1check: 2 x 2 x 3 x 5 = 60

Step 3 — Divide by 2

Divide by the next prime: 30 ÷ 2 = 15.

30÷2=1530 \div \hl{2} = 15
30 ÷ 2 = 15; collect 2.numberdivide bynext6023030215??????factor chips22final productwait until the ladder reaches 1check: 2 x 2 x 3 x 5 = 60

Step 4 — Divide by 3

Divide by the next prime: 15 ÷ 3 = 5.

15÷3=515 \div \hl{3} = 5
15 ÷ 3 = 5; collect 3.numberdivide bynext60230302151535???factor chips223final productwait until the ladder reaches 1check: 2 x 2 x 3 x 5 = 60

Step 5 — Divide by 5

Divide by the next prime: 5 ÷ 5 = 1.

5÷5=15 \div \hl{5} = 1
5 ÷ 5 = 1; collect 5.numberdivide bynext60230302151535551factor chips2235final productwait until the ladder reaches 1check: 2 x 2 x 3 x 5 = 60

Step 6 — Result

Read the final result.

60=22×3×560 = 2^{2} \times 3 \times 5
All factors collected: 2^2 x 3 x 5.numberdivide bynext60230302151535551factor chips2235final product60 = 2^2 x 3 x 5check: 2 x 2 x 3 x 5 = 60
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.