Maths / Numbers
Prime Factorisation Calculator
Break a number into its prime factors with exponents, list all its divisors, and find the greatest common divisor (GCD) and least common multiple (LCM) of several numbers.
Prime Factorisation Calculator: The number is divided by 2, by 3, and then by every candidate of the form 6k ± 1 up to its square root, keeping each prime as many times as it divides. Whatever remains above 1 is prime. The divisors come from every combination of the prime factors. The GCD uses Euclid's algorithm, and the LCM is the product divided by the GCD. Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
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- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
360 = 23 × 32 × 5
360 is composite: 6 prime factors, 3 distinct.
24 divisors
1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
Factor trees
On paper, split a number into any two factors and keep splitting until every branch ends in a prime: 360 = 36 × 10 = (6 × 6) × (2 × 5) = 2³ × 3² × 5. Whatever the first split, the primes at the ends are always the same.
To simplify fractions with the GCD, use the fraction calculator; for practice sheets, the maths worksheet generator.
Counting divisors
Add one to each exponent and multiply: 360 = 2³ × 3² × 5¹ has (3 + 1) × (2 + 1) × (1 + 1) = 24 divisors.
How to use it
- Enter a whole number, up to about nine quadrillion.
- Read its prime factorisation, such as 360 = 2³ × 3² × 5, and its divisors.
- Add other numbers to find their GCD and LCM.
Privacy & limitations
The calculation runs in your browser.
Related tools
Frequently asked questions
Is 1 a prime number?
No: a prime has exactly two divisors, 1 and itself, and 1 has only one. 2 is the only even prime.
How do GCD and LCM help with fractions?
Divide the top and bottom of a fraction by their GCD to simplify it; use the LCM of the denominators as the common denominator to add fractions.
How large a number can it factor?
Any whole number up to 9,007,199,254,740,991, the largest integer a browser handles exactly; very large numbers with two big prime factors take a moment.
Free tool · runs in your browser · no account required