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:
- 2 is a factor because 6 is even.
- 3 is a factor because 5 + 7 + 6 = 18, which is divisible
- 6 is a factor because 2 and 3 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:
is the prime factorization of 72?
Throw some tinsel on that tree, and you’ve got yourself
a Christmas party.