# 1.5 Greatest Common Factor And Least Common Multiple Worksheet With Answers - College Of The Sequoias

1.5 Greatest Common Factor and Least Common Multiple
This chapter will conclude with two topics which will be used when working with fractions.
Recall that factors of a number are numbers that divide into it. For example, the factors of the
numbers 18 and 24 are:
factors of 18: 1, 2, 3, 6, 9, 18
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The greatest common factor (abbreviated GCF) is the largest common factor. That is, it is the
largest factor common to both lists. A quick survey of the factors indicates the GCF of 18 and 24
must be 6, since it is a factor in each list, and it is the largest such factor common to both lists. If
three numbers are used, we still find the common factor to all three lists. For example, the factors
of the numbers 24, 32, and 80 are:
factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
factors of 32: 1, 2, 4, 8, 16, 32
factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The GCF of 24, 32, and 80 must be 8, since it is the largest number common to both lists.
Example 1
Find the greatest common factor of each set of numbers by listing factors.
a.
12, 18
b.
24, 30
c.
40, 60
d.
12, 24, 40
Solution
a.
Begin by listing the factors of 12 and 18:
factors of 12: 1, 2, 3, 4, 6, 12
factors of 18: 1, 2, 3, 6, 9, 18
Since 6 is the largest number common to both lists, the GCF of 12 and 18
is 6. Note that 2 and 3 are also common factors, but they are not the greatest
common factor (largest such common factor).
40