Prime Factorization Calculator · Practical guide
Prime Factorization of 360
360 breaks down to 2^3 × 3^2 × 5 — here is every step of the division.
At a glance
The Answer
The prime factorization of 360 is 2^3 × 3^2 × 5 — that is, 2 × 2 × 2 × 3 × 3 × 5. Because it has prime factors other than itself, 360 is a composite number, not a prime.
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Result
The Division Steps
| Step | Divide By | Result |
|---|---|---|
| 360 | 2 | 180 |
| 180 | 2 | 90 |
| 90 | 2 | 45 |
| 45 | 3 | 15 |
| 15 | 3 | 5 |
| 5 | 5 | 1 — done |
The Factor Tree
Splitting off the smallest prime each time, the tree branches like this:
360
├── 2
├── 180
├── 2
└── 90 → 2 × 45 → 3 × 15 → 3 × 5
Collecting the leaves — 2, 2, 2, 3, 3, 5 — reproduces the factorization.
Why 360 Has So Many Factors
The exponent form tells you the total number of divisors: add 1 to each exponent and multiply. For 2^3 × 3^2 × 5^1 that is (3+1)(2+1)(1+1) = 24 factors. That abundance of divisors is exactly why 360 shows up in circles, time, and measurement — it divides evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, and more.
Frequently Asked Questions
Is 360 a prime number?
No. 360 factors as 2^3 × 3^2 × 5, so it has many divisors besides 1 and itself, making it composite.
How many factors does 360 have?
Twenty-four. Add 1 to each exponent in 2^3 × 3^2 × 5^1 and multiply: 4 × 3 × 2 = 24.
What are the distinct prime factors of 360?
Just 2, 3, and 5. The factorization repeats 2 three times and 3 twice, but only three different primes are involved.
Why start dividing by 2?
Trial division works from the smallest prime upward. Pulling out 2s first keeps every intermediate number as small as possible and guarantees you find factors in order.