Prime factorization calculator
Calculator
The calculator needs JavaScript. The tables below give the same numbers for common cases.
How it is worked out
- Divide by the smallest prime that fits, again and again, until 1 is left.
- 360 ÷ 2 = 180; 180 ÷ 2 = 90; 90 ÷ 2 = 45; 45 ÷ 3 = 15; 15 ÷ 3 = 5; 5 ÷ 5 = 1
| Inputs | Answer |
|---|---|
| Whole number: 360 | 360 = 2 × 2 × 2 × 3 × 3 × 5. |
| Whole number: 84 | 84 = 2 × 2 × 3 × 7. |
| Whole number: 97 | 97 is a prime number. |
| Whole number: 1001 | 1,001 = 7 × 11 × 13. |
How to use it
Every whole number above 1 is either prime or a product of primes in exactly one way (the fundamental theorem of arithmetic). The calculator divides by the smallest prime that fits, again and again, until nothing is left. 360 = 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5.
The number of divisors is the product of (exponent + 1) over the prime powers: 360 has (3 + 1)(2 + 1)(1 + 1) = 24 divisors.
Frequently asked questions
What is the prime factorization of 360?
2³ × 3² × 5.
How many divisors does 360 have?
24, from (3 + 1)(2 + 1)(1 + 1).
Is 1 a prime number?
No. A prime has exactly two divisors, and 1 has only one.
Method: standard arithmetic shown step by step; no outside data is used. Checked 2026-11-12.
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General information only. Results are plain arithmetic on the numbers you enter; check anything important (money, health, school work) against your own records or the official source.