Prime Factorization Tree

Prime factorization breaks a whole number down into the prime numbers that multiply together to make it — the one decomposition every composite number has, and exactly one. This tool takes any integer of 2 or more and factors it for real, then draws the result as the branching factor tree taught in school: start with the number, split off its smallest prime factor, and keep splitting the remaining piece until only primes are left.

The splitting rule is trial division by the smallest possible prime at every step: try 2 first, then odd numbers 3, 5, 7, 9... up to the square root of the current value. For 360 that plays out as 360 = 2 × 180, then 180 = 2 × 90, then 90 = 2 × 45, then 45 = 5 × 9, then 9 = 3 × 3 — five splits ending in six prime leaves (2, 2, 2, 3, 3, 5). Tallying those leaves gives the compact exponent form shown under the diagram: 360 = 2³ × 3² × 5.

All of this runs with exact BigInt arithmetic, so there is never any floating-point rounding on the way down. Trial division up to the square root is fast for everyday numbers but does get slower the larger the input's smallest prime factor is, so the tool caps input at 1,000,000,000,000 (10^12) and reports an honest message beyond that rather than freezing the tab — a browser has no business hanging on a giant semiprime just to prove a point.

A visual factor tree is the standard way prime factorization is taught in school, and it stays useful well past the classroom: reducing fractions, finding the greatest common factor or least common multiple by comparing prime powers, simplifying square roots, and spot-checking whether a number is prime all come back to the same decomposition. Everything runs locally in your browser — no sign-up, no server round-trip.