What Is the Prime Factorization of 72?
72 = 2 × 2 × 2 × 3 × 3, which is written 2³ × 3² with exponents. Every number in that product is prime, so it cannot be broken down any further. The prime factors of 72 are 2, 3.
Division Ladder for 72
Divide by the smallest prime that goes in, write the answer, and repeat until you reach 1.
- 72 ÷ 2 = 36
- 36 ÷ 2 = 18
- 18 ÷ 2 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1
The numbers in bold are the prime factors: 2 × 2 × 2 × 3 × 3.
Write It with Exponents
- 2 appears 3 times, written 2³
- 3 appears 2 times, written 3²
Put together: 72 = 2³ × 3².
Check by Multiplying Back
2 × 2 × 2 × 3 × 3 = 72. It matches the number we started with, so the factorization is right.
Count the Factors of 72
Add 1 to each exponent and multiply: (3 + 1) × (2 + 1) = 12. So 72 has 12 factors:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
See them paired up on the factors of 72 page.
Prime or composite?
72 is composite, because it has more than two factors. Try another number in the Prime Factorization Calculator.