1.5 Greatest Common Factor And Least Common Multiple Worksheet With Answers - College Of The Sequoias Page 2
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11b.
Begin by listing the factors of 24 and 30:
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Since 6 is the largest number common to both lists, the GCF of 24 and 30
is 6.
c.
Begin by listing the factors of 40 and 60:
factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
factors of 60: 1, 2, 3, 4, 6, 10, 15, 20, 30, 60
Since 20 is the largest number common to both lists, the GCF of 40 and 60
is 20.
d.
Begin by listing the factors of 12, 24, and 40:
factors of 12: 1, 2, 3, 4, 6, 12
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Since 4 is the largest number common to all three lists, the GCF of 12, 24,
and 40 is 4.
Though this method of finding the GCF seems reasonable, when the numbers get larger it can
become quite difficult to list all of the factors of two numbers. For example, suppose we wanted
to find the GCF of 84 and 120. We will investigate an approach using prime numbers. Let’s
begin by finding the prime factorizations of 84 and 120:
(
)
(
)
84 = 4 • 21 = 2 • 2
= 2 • 2 • 3 • 7
• 3 • 7
(
)
(
)
(
)
(
)
120 = 10 • 12 = 2 • 5
= 2 • 5
= 2 • 2 • 2 • 3 • 5
• 4 • 3
• 2 • 2 • 3
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