Break a number into its prime factors.
Divide repeatedly by the smallest prime that fits until you reach 1. 360 = 2³ × 3² × 5.
Every whole number greater than 1 is either prime or can be written as a product of primes in exactly one way. This calculator finds that factorization for any number up to a quadrillion, shows it in exponent form, lists the division steps, says whether the number is prime and gives the number and sum of its divisors.
Prime factors are the basis of the GCF and LCM. See the Factor Calculator, GCF Calculator and LCM Calculator; for huge integers try the Big Number Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| Prime factors (with repeats) | 2 × 2 × 2 × 3 × 3 × 5 |
| Exponent form | 2³ × 3² × 5 |
| Distinct primes | 3 |
| Total prime factors | 6 |
| Number of divisors | 24 |
| Sum of divisors | 1,170 |
| Prime? | No — composite |
| Divide by the next prime | Quotient |
|---|---|
| 360 ÷ 2 | 180 |
| 180 ÷ 2 | 90 |
| 90 ÷ 2 | 45 |
| 45 ÷ 3 | 15 |
| 15 ÷ 3 | 5 |
| 5 ÷ 5 | 1 |
| Number | Prime factors |
|---|---|
| 60 | 2² × 3 × 5 |
| 360 | 2³ × 3² × 5 |
| 1001 | 7 × 11 × 13 |
| 1024 | 2¹⁰ |
| 123456 | 2⁶ × 3 × 643 |
| Range | Primes |
|---|---|
| 1–25 | 2, 3, 5, 7, 11, 13, 17, 19, 23 |
| 26–50 | 29, 31, 37, 41, 43, 47 |
| 51–75 | 53, 59, 61, 67, 71, 73 |
| 76–100 | 79, 83, 89, 97 |
Writing a number as a product of prime numbers, such as 360 = 2³ × 3² × 5.
Yes — by the Fundamental Theorem of Arithmetic, apart from the order of the factors.
Split the number into any two factors, then keep splitting each factor until every branch ends in a prime.
If no prime up to its square root divides it, it is prime. The calculator reports it directly.
Up to 10¹⁵ (one quadrillion), instantly in your browser.
It underlies fractions, GCF and LCM, and the security of RSA encryption depends on how hard it is to factor very large numbers.
It uses the standard method: n = p₁^a₁ × p₂^a₂ × … × pₖ^aₖ divisors = (a₁ + 1)(a₂ + 1)…(aₖ + 1) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
No. Everything is calculated in your browser and nothing you enter is uploaded or saved.
