TUTORIALS:

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.
Finding Factors
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.
EXAMPLE 1
Find all the factors of 6.
Solution
Starting with 1, we divide each whole number into 6.
So the factors of 6 are 1, 2, 3, and 6. Note that
 1 is a factor of 6 and that
 6 is a factor of 6.
 We did not need to divide 6 by the numbers 7 or greater.
The reason is that no numberlarger than 6 could divide
evenly into 6, that is, divide into 6 with no remainder.
TIP
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.
The number is
divisible by 
if

2 
the ones digit is 0, 2, 4, 6, or 8, that
is, if the number is even. 
3 
the sum of the digits is divisible by 3. 
4 
the number named by the last two digits
is divisible by 4. 
5 
the ones digit is either 0 or 5. 
6 
the number is even and the sum of the
digits is divisible by 3. 
9 
the sum of the digits is divisible by 9. 
10 
the ones digit is 0. 
Note that divisibility by 6 is equivalent to divisibility by
both 2 and 3.
