Factors and Multiples
In this discussion we will only deal with the natural numbers (that is, positive integers): 1, 2, 3, 4, 5, …
If m = d×q we say d is a factor of m, and m is a multiple of d.
Note: d divides m so d is also called a divisor of m.
Since m = 1×m, 1 and m are both factors of m. The number 1 is called the trivial factor as every number is divisible by 1. m is called the improper factor as every number is also divisible by itself.
A number that has a nontrivial proper factor is said to be composite.
Remark: Suppose and then . Thus to discover the factors of a number m we need only test with numbers .
12 = 3 x 4 = 6 x 2 = 12 x 1
1, 2, 3, 4, 6 and 12 are factors of 12. 12 is a multiple of 1, 2, 3, 4, 6 and 12. 1 is a trivial factor. 12 is an improper factor. 2, 3, 4 and 6 are nontrivial proper factors so 12 is composite.
Find a non-trivial proper factor of the given number. If none exists, enter none.