Chapter 4 Fractions, Decimals, And Percents - Lesson 4-2 Greatest Common Factor Worksheet Page 2
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4Reading Math
Find the GCF of Three Numbers
Greatest Common Factor
The greatest common factor
2
Find the GCF of 12, 24, and 60.
is also called the greatest
common divisor because it
Write the prime factorization. Circle the common prime factors.
is the greatest number that
12 =
2
×
2
×
3
divides evenly into the given
numbers.
24 =
×
× 2 ×
2
2
3
Write the prime factorization of 12, 24, and 60.
60 =
2
×
2
×
3
× 5
The common prime factors are 2, 2, and 3. So, the GCF is 2 × 2 × 3, or 12.
Find the GCF of each set of numbers.
30, 45, 75 15
42, 70, 84 14
d.
e.
3
SCHOOL SPIRIT
The cheerleaders are
making spirit ribbons. Blue ribbon comes
in a 24 inch spool, red ribbon comes in a
24 in.
30 inch spool, and gold ribbon comes in
a 36 inch spool. The cheerleaders want to
30 in.
cut strips of equal length and use the
entire spool of each ribbon. What is the
36 in.
length of the longest piece of ribbon that
can be cut from each spool?
The length of the longest ribbon that can be cut from each spool
is the GCF of the three lengths.
24 =
2
× 2 × 2 ×
3
30 =
×
× 5
2
3
Write the prime factorization of 24, 30, and 36.
36 =
× 2
×
× 3
2
3
The GCF of 24, 30, and 36 is 2 × 3 or 6. So, the ribbons should be
6 inches long.
4
How many spirit ribbons can be made if the ribbons are cut into
6-inch pieces?
There is a total of 24 + 30 + 36, or 90 inches of ribbon.
So, 90 ÷ 6, or 15 spirit ribbons can be made.
Prime Numbers
Prime Numbers
The GCF of a group of
prime numbers is 1.
CARPENTRY
Mr. Glover wants to make shelves for his garage using
f.
an 18-foot board and a 36-foot board. He will cut the boards to
make shelves of the same length and wants to use all of both
boards. Find the longest possible length of each shelf. How many
shelves can he make? 18 ft, 3
187
Lesson 4-2 Greatest Common Factor
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