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Greatest Common Factor - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=8

Find the greatest common factor of each pair of numbers.

 1.   6, 8 2.   4, 6

Complexity=12

Find the greatest common factor of each pair of numbers.

 1.   12, 3 2.   6, 9

Complexity=20

Find the greatest common factor of each pair of numbers.

 1.   14, 6 2.   8, 20

Complexity=30

Find the greatest common factor of each pair of numbers.

 1.   16, 28 2.   30, 18

Complexity=40

Find the greatest common factor of each pair of numbers.

 1.   24, 28 2.   36, 30

Complexity=50

Find the greatest common factor of each pair of numbers.

 1.   40, 26 2.   30, 24

Complexity=80

Find the greatest common factor of each pair of numbers.

 1.   70, 80 2.   48, 54

Complexity=150

Find the greatest common factor of each pair of numbers.

 1.   72, 112 2.   143, 110

Complexity=8

Find the greatest common factor of each pair of numbers.

16, 8
Solution
8 - 6 = 2. Does 2 divide evenly into 6? Yes. Therefore 2 is the GCF.

Factors of 6: 1, 2, 3, 6
Factors of 8: 1, 2, 4, 8

24, 6
Solution
6 - 4 = 2. Does 2 divide evenly into 4? Yes. Therefore 2 is the GCF.

Factors of 4: 1, 2, 4
Factors of 6: 1, 2, 3, 6

Complexity=12

Find the greatest common factor of each pair of numbers.

112, 3
Solution
3 divides evenly into 12. Therefore 3 must be the greatest common factor.

Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 3: 1, 3

26, 9
Solution
9 - 6 = 3. Does 3 divide evenly into 6? Yes. Therefore 3 is the GCF.

Factors of 6: 1, 2, 3, 6
Factors of 9: 1, 3, 9

Complexity=20

Find the greatest common factor of each pair of numbers.

114, 6
Solution
14 - 6 = 8. GCF(14,6) = GCF(6, 8).
The difference between 6 and 8 is 2. Does 2 divide evenly into 8? Yes. Therefore 2 is the GCF.

Factors of 14: 1, 2, 7, 14
Factors of 6: 1, 2, 3, 6

28, 20
Solution
20 - 8 = 12. GCF(20,8) = GCF(8, 12).
The difference between 8 and 12 is 4. Does 4 divide evenly into 12? Yes. Therefore 4 is the GCF.

Factors of 8: 1, 2, 4, 8
Factors of 20: 1, 2, 4, 5, 10, 20

Complexity=30

Find the greatest common factor of each pair of numbers.

116, 28
Solution
28 - 16 = 12. GCF(28,16) = GCF(16, 12).
The difference between 16 and 12 is 4. Does 4 divide evenly into 12? Yes. Therefore 4 is the GCF.

Factors of 16: 1, 2, 4, 8, 16
Factors of 28: 1, 2, 4, 7, 14, 28

230, 18
Solution
30 - 18 = 12. GCF(30,18) = GCF(18, 12).
The difference between 18 and 12 is 6. Does 6 divide evenly into 12? Yes. Therefore 6 is the GCF.

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 18: 1, 2, 3, 6, 9, 18

Complexity=40

Find the greatest common factor of each pair of numbers.

124, 28
Solution
28 - 24 = 4. Does 4 divide evenly into 24? Yes. Therefore 4 is the GCF.

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 28: 1, 2, 4, 7, 14, 28

236, 30
Solution
36 - 30 = 6. Does 6 divide evenly into 30? Yes. Therefore 6 is the GCF.

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Complexity=50

Find the greatest common factor of each pair of numbers.

140, 26
Solution
The factors of 26 are 1, 2, 13, 26.
From greatest to least, check if each factor divides evenly into 40.
26 does not divide evenly into 40.
13 does not divide evenly into 40.
2 divides evenly into 40. Therefore, 2 is the GCF.

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 26: 1, 2, 13, 26

230, 24
Solution
30 - 24 = 6. Does 6 divide evenly into 24? Yes. Therefore 6 is the GCF.

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Complexity=80

Find the greatest common factor of each pair of numbers.

170, 80
Solution
80 - 70 = 10. Does 10 divide evenly into 70? Yes. Therefore 10 is the GCF.

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

248, 54
Solution
54 - 48 = 6. Does 6 divide evenly into 48? Yes. Therefore 6 is the GCF.

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54

Complexity=150

Find the greatest common factor of each pair of numbers.

172, 112
Solution
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
From greatest to least, check if each factor divides evenly into 112.
72 does not divide evenly into 112.
36 does not divide evenly into 112.
24 does not divide evenly into 112.
18 does not divide evenly into 112.
12 does not divide evenly into 112.
9 does not divide evenly into 112.
8 divides evenly into 112. Therefore, 8 is the GCF.

Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112

2143, 110
Solution
The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110.
From greatest to least, check if each factor divides evenly into 143.
110 does not divide evenly into 143.
55 does not divide evenly into 143.
22 does not divide evenly into 143.
11 divides evenly into 143. Therefore, 11 is the GCF.

Factors of 143: 1, 11, 13, 143
Factors of 110: 1, 2, 5, 10, 11, 22, 55, 110   