Quick answer: 360 = 2³ × 3² × 5: divide by 2 three times (360 → 180 → 90 → 45), by 3 twice (45 → 15 → 5) and by 5 once.
How it's calculated
Divide by the smallest prime that goes in exactly (2, then 3, 5, 7, 11 …) and repeat on the result until you reach 1. The primes you divided by are the prime factors.
Every whole number above 1 has exactly one prime factorization (the fundamental theorem of arithmetic). If no prime up to the square root divides the number, it is prime.
The exponents give the number of divisors: for 2³ × 3² × 5 there are (3 + 1)(2 + 1)(1 + 1) = 24. Prime factors also give the GCF and LCM; all the divisors are listed in the factor calculator.
Worked examples
- 360: 2 × 2 × 2 × 3 × 3 × 5 = 2³ × 3² × 5
- 84: 2² × 3 × 7
- 97: 97 is prime
Frequently asked questions
Is 1 a prime number?
No. A prime has exactly two different factors, 1 and itself; 1 has only one factor.
Does the order of the factors matter?
No. 2³ × 3² × 5 and 5 × 3² × 2³ are the same factorization; it is usually written from the smallest prime up.
How large a number can I factor?
Up to one trillion (10¹²), by trial division in your browser.
What is the prime factorization of 360?
2³ × 3² × 5. Halve 360 three times to get 45, divide by 3 twice, and you're left with 5.
How many divisors does 360 have?
24. Add 1 to each exponent and multiply them together: 4 × 3 × 2.
Is 91 a prime number?
No, though it looks like one. 91 is 7 × 13.