Factors and Prime Numbers
What Factors Mean and Why They Are Important
Recall that in a multiplication problem, the whole numbers that we are multiplying are called factors. For instance, 2 is said to be a factor of 8 because 2 Â· 4 = 8. Likewise, 4 is a factor of 8.
Another way of expressing the same idea is in terms of division: We say that 8 is divisible by 2, meaning that there is a remainder 0 when we divide 8 by 2.
Note that 1, 2, 4, and 8 are all factors of 8.
Although we factor whole numbers, a major application of factoring involves working with fractions, as we demonstrate in the next section.
To identify the factors of a whole number, we divide the whole number by the numbers 1, 2,3, 4, 5, 6, and so on, looking for remainders of 0.
Find all the factors of 6.
Starting with 1, we divide each whole number into 6.
So the factors of 6 are 1, 2, 3, and 6. Note that
For any whole number, both the number itself and 1 are always factors. Therefore all whole numbers (except 1) have at least two factors.
When checking to see if one number is a factor of another, it is generally faster to use the following divisibility tests than to divide.
Note that divisibility by 6 is equivalent to divisibility by both 2 and 3.