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Greatest Common Factor

Introduction

Terms

Factor - a factor is any number that can divide into another without leaving a remainder. Since 2 * 3 = 6, 2 and 3 are both factors of 6.
Divisor - Another way of referring to a factor.
Greatest Common Factor - A greatest common factor (or GCF) is the highest factor that is the same between two or more numbers.
Highest Common Factor - Another way of referring to GCF.

Lesson

A Greatest Common Factor (also seen as GCF or HCF) is the highest factor that is the same for two or more numbers. It is easy to figure out the GCF when you split the two numbers up into their factors. For example, if we are told to find the GCF of 15 and 20, we first split 15 and 20 into their factors.

Factors of 15 are 1, 3, 5, 15

Factors of 20 are 1, 2, 4, 5, 10, 20

The factors that appear in both lists are 1 and 5. The greatest of these is 5, so 5 is the Greatest Common Factor of 15 and 20.

Examples

Greatest Common Factor (Example #1)

20 and 3020\text{ and }30
First list the factors of the number (the numbers that divide each number with zero remainder)
Divisors of 20 are: 1, 2, 4, 5, 10, 20
Divisors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The largest number that divides 20 and 3020\text{ and }30 is 1010, so the GCF = 1010

Greatest Common Factor (Example #2)

18 and 1918\text{ and }19
First list the factors of the number (the numbers that divide each number with zero remainder)
Divisors of 18 are: 1, 2, 3, 6, 9, 18
Divisors of 19 are: 1, 19
The largest number that divides 18 and 1918\text{ and }19 is 11, so the GCF = 11

Greatest Common Factor (Example #3)

25 and 5025\text{ and }50
First list the factors of the number (the numbers that divide each number with zero remainder)
Divisors of 25 are: 1, 5, 25
Divisors of 50 are: 1, 2, 5, 10, 25, 50
The largest number that divides 25 and 5025\text{ and }50 is 2525, so the GCF = 2525

Greatest Common Factor (Example #4)

10,15 and 2010, 15\text{ and }20
First list the factors of the number (the numbers that divide each number with zero remainder)
Divisors of 10 are: 1, 2, 5, 10
Divisors of 15 are: 1, 3, 5, 15
Divisors of 20 are: 1, 2, 4, 5, 10, 20
The largest number that divides 10,15 and 2010, 15\text{ and }20 is 55, so the GCF = 55

Greatest Common Factor Worksheets (PDF)

Greatest Common Factor Worksheet 1

Greatest Common Factor Worksheet 2

Greatest Common Factor Worksheet 3

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