Factor Finding Mission

Intro to Proofs · Axiom Academy

Every whole number is built from smaller pieces. Your mission: find them — and meet the one rule that decides what divides what. Numbers come apart into factors A factor of a number divides it evenly, with nothing left over. But factors hide more factors inside them: split a number, split the pieces, and keep going, and you always bottom out at the same place — the primes the number is built from. That bedrock is the start of nearly everything in number theory. Watch 60 come apart. It splits into a pair of factors, each composite piece splits again, and the tree stops only when every leaf is a prime that can't be broken further. Read the bottom row left to right and you have the prime factorization. No matter which factor you split first, the leaves are always the same primes — that's the Fundamental Theorem of Arithmetic. Pick a number. Every divisor that goes in evenly lights up, and the toy pairs them off — small factor with its partner — so each pair multiplies right back to your number. Watch how the factors of 36 crowd in while a prime like 37 has almost none. Factors come in pairs — that's why a perfect square like 36 has an odd count: one pair ( ) is a number paired with itself. What "divides evenly" really means Behind every factor is one rule. Divide any a by any b and you always get a quotient q and a leftover r with . The divisor b is a factor of a exactly when that remainder r hits 0 . Slide both numbers and watch the remainder decide.

This is the written version of the interactive lesson above. See the full Intro to Proofs course.