justyourcalculatorPrime Factorization Calculator
Break a number into primes, with a factor tree and every division.
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Prime Factorization Calculator
Prime factors with a factor tree
Prime factorization of 360
2³ × 3² × 5
2 × 2 × 2 × 3 × 3 × 5
- Prime?
- No, composite
- Distinct prime factors
- 2, 3, 5
- Number of prime factors (with repeats)
- 6
- Number of divisors
- 24
How it was calculated
- Factor tree: 360 ├─ 2 └─ 180 ├─ 2 └─ 90 ├─ 2 └─ 45 ├─ 3 └─ 15 ├─ 3 └─ 5
- Division ladder (divide by the smallest prime each time):
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
- 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
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How the prime factorization calculator works
Every whole number above 1 is either prime or can be written as a product of primes in exactly one way (the fundamental theorem of arithmetic). That product is its prime factorization: 360 = 2³ × 3² × 5.
To find it, divide by the smallest prime that goes in evenly (2, then 3, 5, 7, ...) and keep dividing the result until you reach 1. The factor tree shows the same process as branches, and you only need to test primes up to the square root of what's left.
Prime factorizations make it easy to find the GCF, the LCM, the number of divisors, and to simplify roots.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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