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 Depdendent Variable

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 Dependent Variable

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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.