Intermediate Test Prep Math 5 Uses of Factoring

Uses of Factoring
Lesson

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Let's review a few things about factors! Let's start with the definition!!!!

Factor: A number that divides evenly into another number (without a remainder).

You can find the factors of any number by asking yourself the question: What numbers will divide evenly into the number?

Examples

factors of 8 are {1,2,4, and 8}
factors of 12 are {1,2,3,4,6, and 12}
factors of 20 are {1,2,4,5,10, and 20}

Each of the factors inside the { } divide evenly into the number.

Can you make some generalizations about the above numbers and their factors?

Let's look at the above examples again for pairs.

If a number is a perfect square, the middle factor will be multiplied (or paired) with itself!

After finding each number's factors, you can then find the common factors and then the greatest common factor (GCF).

number factors common factors GCF

12 1,2,3,4,6,12 1,2,3,6, 6

18 1,2,3,6,9,18

24 1,2,3,4,6,8,12,24

Greatest Common Factor is used to put fractions in simplest form.

12 ÷ 6 = 2
18 6 3

18 ÷ 6 = 3
24 6 4

Let's try some more! Here are two more numbers with common factors.

number	factors	common factors	GCF
20	1,2,4,5,10,20	1,2,4	4
32	1,2,4,8,16,32	1,2,4	4

20 ÷ 4 = 5
32 4 = 8

Let's Practice!

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