Prime Factorization Calculator
Break a number into its prime factors, with each division shown.
About the Prime Factorization Calculator
Every whole number above 1 is either prime or a unique product of primes (the fundamental theorem of arithmetic). Divide by the smallest prime that fits, repeat with the result, and stop at 1.
The formula
n = p₁^a × p₂^b × p₃^c × …
- p
- prime numbers in increasing order
- a, b, c
- how many times each divides n
Worked example
8,400
- 8,400 = 2⁴ × 3 × 5² × 7
Questions people ask
Is 1 a prime number?
No. A prime has exactly two factors, 1 and itself; 1 has only one.
What's a factor tree?
A diagram of the same process: split the number into two factors, and keep splitting until every branch ends in a prime.