This math topic focuses on identifying the Greatest Common Factor (GCF) of pairs of numbers by finding their shared prime factors. It's a foundational step in a broader introductory unit on factoring and identifying greatest common factors. Each problem in the set provides pairs of numbers for which students must choose the correct set of common prime factors from multiple options. The practice helps reinforce the ability to break down numbers into their prime components and identify those that are common to both numbers in the pair.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Finding Greatest Common Factor Shared Factors Worksheet

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Finding Greatest Common Factor Shared Factors
1
Find the shared prime factors of these numbers
4, 12
a
{2, 2}
b
{7, 2, 7, 4, 3}
c
{2, 5, 4, 3}
d
{2, 6, 6, 7}
e
{2, 6, 4, 6, 3}
f
{2}
2
Find the shared prime factors of these numbers
12, 9
a
{7, 2, 6, 4}
b
{3, 5, 3, 7, 5}
c
{3, 5, 6, 7}
d
{6, 2, 4, 6}
e
{4}
f
{3}
3
Find the shared prime factors of these numbers
8, 12
a
{4, 2, 7, 4, 4}
b
{2, 2, 4}
c
{6, 2, 6, 2, 4}
d
{2, 2}
e
{7, 2}
f
{2, 6}
4
Find the shared prime factors of these numbers
10, 8
a
{2, 3}
b
{4, 6, 2}
c
{5, 3, 5, 6}
d
{2}
e
{7, 4, 5, 3}
f
{4, 4, 4}
5
Find the shared prime factors of these numbers
6, 10
a
{2, 2}
b
{4, 4, 5}
c
{2}
d
{6}
e
{2, 7, 6}
f
{5}
6
Find the shared prime factors of these numbers
12, 2
a
{2, 5, 6, 3, 6}
b
{6}
c
{2, 2, 3, 5, 2}
d
{2, 5, 4}
e
{2, 2}
f
{2}
7
Find the shared prime factors of these numbers
10, 4
a
{2}
b
{6}
c
{2, 2, 2}
d
{6, 7, 2}
e
{2, 7}
f
{2, 5, 6}
8
Find the shared prime factors of these numbers
4, 10
a
{2, 6, 5}
b
{6, 5, 2, 7}
c
{2}
d
{2, 6}
e
{3, 7, 6}
f
{5}