What Is the Prime Factorization of 360?
360 = 2 × 2 × 2 × 3 × 3 × 5, which is written 2³ × 3² × 5 with exponents. Every number in that product is prime, so it cannot be broken down any further. The prime factors of 360 are 2, 3, 5.
Division Ladder for 360
Divide by the smallest prime that goes in, write the answer, and repeat until you reach 1.
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
The numbers in bold are the prime factors: 2 × 2 × 2 × 3 × 3 × 5.
Write It with Exponents
- 2 appears 3 times, written 2³
- 3 appears 2 times, written 3²
- 5 appears 1 time, written 5
Put together: 360 = 2³ × 3² × 5.
Check by Multiplying Back
2 × 2 × 2 × 3 × 3 × 5 = 360. It matches the number we started with, so the factorization is right.
Count the Factors of 360
Add 1 to each exponent and multiply: (3 + 1) × (2 + 1) × (1 + 1) = 24. So 360 has 24 factors:
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
See them paired up on the factors of 360 page.
Prime or composite?
360 is composite, because it has more than two factors. Try another number in the Prime Factorization Calculator.