Download 2-7 Greatest Common Factor (GCF)

2-7 Greatest Common Factor (GCF)
Common Factor: a whole number that is a factor of two or more nonzero whole numbers
Example: Factors of 12  ________________________
Factors of 18  ________________________
Common factors
of 12 and 18 are: _________________.
Greatest Common Factor (GCF): the greatest of the common factors
Example: GCF of 12 and 18  ________
Relatively Prime: two or more numbers whose GCF is 1
Examples: 28 and 45, 3 and 20,
39 and 44
Three Methods
There are three methods to find the GCF of a numbers: make a list, upside-down division and prime
factorization.
Make a list method:
List the factors of each number and select the greatest one that they have in common.
Example: Find the GCF of 48, 24, and 36
Factors of 48  _____________________________
Factors of 24  _____________________________
Factors of 36  _____________________________
Upside-down division method: This method only works with two numbers.
Find the GCF of 42 and 70.
2 42 70
7 21 35
3 5
Use upside-down division symbols to
divide both numbers at the same time.
When dividing, use only prime factors.
 Done when relatively prime
GCF of 42 and 70  2  7 = 14
The upside-down division is complete when
the two numbers are relatively prime.
The GCF is the product of the prime factors
along the side.
More upside-down division examples:
36 90
48 90
GCF of 36 and 90  _______________
GCF of 48 and 90  _______________
Prime Factorization method:
Write the prime factorization of each number. Identify the common factors. The GCF is the
product of the common factors.
42 = 2  3  7
70 = 2  5  7
GCF of 42 and 70  ____________________
More prime factorization examples:
180 = 2  2  3  3  5
126 = 2  3  3  7
GCF of 180 and 126  ___________________
You may also use exponents when writing the prime factorizations. In this case, the GCF is the
product of the common factors with the lowest exponent.
Example:
180 = 22  32  5
GCF of 180 and 126  ___________________
126 = 2  32

7
Example:
16 =
24 =
30 =
GCF of 16, 24 and 30  ___________________