An integer is called a factor if it divides another integer evenly. For example, 3 is one of the factors of 6, because .

There’s no magic formula to determine the factors of any given number, although the divisibility rule on the previous page can help. For example, for the number 576, you know that the following numbers are factors:

All even numbers have 2 as a factor. Lucky them. All prime numbers have two and only two factors: 1 and the number itself. Think of prime numbers as loners of sorts. The number 2 is the only even prime number. All other prime numbers are odd.

As its name suggests, prime factorization involves using prime factors. Prime factorization is like taking apart a bicycle until you have every individual piece as small as it can get: the chain, the seat, the handlebars, and so forth. To find the prime factorization of a number, you divide it and all its factors until every remaining integer is a prime number. The easiest way to solve for prime factorization is to make a pretty little tree:

Throw some tinsel on that tree, and you’ve got yourself a Christmas party.