Math 7 ­ GCF (chapter 5­2)
Greatest Common Factor
(Math 7)
GCFà The largest factor a set of
numbers has in common.
à Think small…
Find the GCF using any method.
1.) 28, 42
2.) 12, 16, 20
3.) 24, 30, 36
Find the GCF of each set of
monomials.
1.) 5t, 15t2
List Method à List the factors
of each number, from least to
greatest, and find the largest factor
all of the numbers have in common.
Factor Tree
• Find the prime factorization for
each of the numbers.
• Circle and list any factors all of the
numbers have in common.
• Multiply those factors.
• The product is the GCF. This number
should NOT be larger than the
smallest number in the group.
Division Steps
• Find the prime factorization for
each of the numbers.
• Circle and list any factors all of the
numbers have in common.
• Multiply those factors.
• The product is the GCF. This
number should NOT be larger than
the smallest number in the group.
Upside Down Division
• Place an inverted division sign around
the numbers.
• Find common factors for all of the
numbers (3).
• Divide all of the numbers by that factor
- the quotient is left in the box.
• Find a common factor(s) for two of the
numbers.
• Divide the two numbers by that factor
& bring down the other numbers.
• To find the GCF - Multiply all of the
divisors along the left-hand side of the
division boxes.
Factor each expression.
• First find a common factor (coefficient
or variable) of the monomials.
• Divide the monomials by that factor.
• Write the common factor on the
outside of the parentheses and leave
the new monomials in the parentheses.
2.) 36a3b, 56a2b2
1
Math 7 ­ GCF (chapter 5­2)
Greatest Common Factor
(Math 7)
GCFà The largest factor a set of
numbers has in common.
à Think small…
Find the GCF using any method.
1.) 28, 42
2.) 12, 16, 20
3.) 24, 30, 36
Find the GCF of each set of
monomials.
1.) 5t, 15t2
List Method à List the factors
of each number, from least to
greatest, and find the largest factor
all of the numbers have in common.
Factor Tree
• Find the prime factorization for
each of the numbers.
• Circle and list any factors all of the
numbers have in common.
• Multiply those factors.
• The product is the GCF. This number
should NOT be larger than the
smallest number in the group.
Division Steps
• Find the prime factorization for
each of the numbers.
• Circle and list any factors all of the
numbers have in common.
• Multiply those factors.
• The product is the GCF. This
number should NOT be larger than
the smallest number in the group.
Upside Down Division
• Place an inverted division sign around
the numbers.
• Find common factors for all of the
numbers (3).
• Divide all of the numbers by that factor
- the quotient is left in the box.
• Find a common factor(s) for two of the
numbers.
• Divide the two numbers by that factor
& bring down the other numbers.
• To find the GCF - Multiply all of the
divisors along the left-hand side of the
division boxes.
Factor each expression.
• First find a common factor (coefficient
or variable) of the monomials.
• Divide the monomials by that factor.
• Write the common factor on the
outside of the parentheses and leave
the new monomials in the parentheses.
2.) 36a3b, 56a2b2
2
Math 7 ­ GCF (chapter 5­2)
3