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Enter a whole number and Axiom breaks it into prime factors, one division at a time.
Enter a whole number of 2 or more and press Factorize. Read the division trail and final product of primes. Numbers up to 1,000,000,000,000 are supported so the divisor search always finishes quickly.
A prime number has exactly two positive factors: 1 and itself. Repeatedly divide by small primes until no composite part remains, then collect repeated factors as powers. Every whole number above 1 has one prime factorization apart from the order of its factors.
60 ÷ 2 = 30, 30 ÷ 2 = 15, and 15 ÷ 3 = 5. The remaining 5 is prime, so 60 = 2² × 3 × 5.
72 ÷ 2 = 36, then 18, then 9; 9 ÷ 3 = 3. Therefore 72 = 2³ × 3². Check: 8 × 9 = 72.
For 13, no smaller prime divides it. Its prime factorization is simply 13; a prime does not need to be split further.
A prime needs two distinct positive factors. The number 1 has only one, so it is neither prime nor composite and has no prime factorization in this tool.
It counts repeated copies of a prime. The factor 2³ means 2 × 2 × 2, not 2 × 3.
No. The input must be a safe whole number at least 2. To study −60 by hand, keep the sign separate and factor its absolute value, 60.
The method tests divisors up to the square root of the remaining number, so a prime near the input limit needs the longest search. That search is capped at about half a million tests, which finishes in a moment; numbers above 1,000,000,000,000 are refused with a message instead of slowing the page down.
Prime factors help explain GCF, LCM, and fraction reduction. Try those related tools, then use the integers lesson to practice recognizing factors and multiples. Related tools: GCF & LCM Calculator, Fraction Calculator. Read the Integers & Negative Numbers lesson or practice integers & negative numbers to build confidence without relying on a calculator.