A factor divides a whole number exactly. A prime is an integer greater than 1 with exactly two positive factors; a composite integer has more than two. Neither 0 nor 1 is prime or composite. The only even prime is 2. Prime factorisation breaks a composite number into prime building blocks. Divide repeatedly by primes until the quotient is 1; retain every repeated factor. Example For 84, successive divisions by 2,2,3,7 give 42,21,7,1. Thus 84=22 x 3 x 7. Multiplying back checks the factorisation. To test 47, it is enough to try primes no larger than sqrt(47): 2,3,5. None divides it, so 47 is prime. If a composite number had both factors above its square root, their product would be too large.

A factor divides a whole number exactly. A prime is an integer greater than \(1\) with exactly two positive factors; a composite integer has more than two. Neither \(0\) nor \(1\) is prime or composite. The only even prime is \(2\).

Prime factorisation breaks a composite number into prime building blocks. Divide repeatedly by primes until the quotient is \(1\); retain every repeated factor.

For \(84\), successive divisions by \(2,2,3,7\) give \(42,21,7,1\). Thus \(84=2^2\times3\times7\). Multiplying back checks the factorisation.

To test \(47\), it is enough to try primes no larger than \(\sqrt{47}\): \(2,3,5\). None divides it, so \(47\) is prime. If a composite number had both factors above its square root, their product would be too large.

Prime factors

Prime factors