\n
\n
1. Decompose the numbers into their prime factors.

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2. \n
3. Underline the factors that all the original numbers have in common.

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4. \n
5. Multiply the underlined numbers to get the GCF.

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6. \n
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## Sample questions

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\n
1. Find the greatest common factor of 12 and 20.

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4. Write down all the factor pairs of 12 and 20:

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Factor pairs of 12: 1 x 12, 2 x 6, 3 x 4

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Factor pairs of 20: 1 x 20, 2 x 10, 4 x 5

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The number 4 is the greatest number that appears in both lists of factor pairs, so its the GCF.

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2. \n
3. Find the greatest common factor of 24, 36, and 42.

\n

6. Decompose all three numbers down to their prime factors:

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24 = 2 x 2 x 2 x 3

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36 = 2 x 2 x 3 x 3

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42 = 2 x 3 x 7

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Underline all factors that are common to all three numbers:

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24 = 2 x 2 x 2 x 3

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36 = 2 x 2 x 3 x 3

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42 = 2 x 3 x 7

\n

\n

2 x 3 = 6

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4. \n
\n

## Practice questions

\n
\n
1. Find the greatest common factor of 10 and 22.

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2. \n
3. Whats the GCF of 8 and 32?

\n
4. \n
5. Find the GCF of 30 and 45.

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6. \n
7. Figure out the GCF of 27 and 72.

\n
8. \n
9. Find the GCF of 15, 20, and 35.

\n
10. \n
11. Figure out the GCF of 44, 56, and 72.

\n
12. \n
\n

Following are the answers to the practice questions:

\n
\n
1. The GCF of 10 and 22 is 2.

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Write down all the factor pairs of 10 and 22:

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10: 1 x 10, 2 x 5

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22: 1 x 22, 2 x 11

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The number 2 is the greatest number that appears on both lists.

\n
2. \n
3. The GCF of 8 and 32 is 8.

\n

Write down all the factor pairs of 8 and 32:

\n

8: 1 x 8, 2 x 4

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32: 1 x 32, 2 x 16, 4 x 8

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The greatest number that appears on both lists is 8.

\n
4. \n
5. The GCF of 30 and 45 is 15.

\n

Write down all the factor pairs of 30 and 45:

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30: 1 x 30, 2 x 15, 3 x 10, 5 x 6

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45: 1 x 45, 3 x 15, 5 x 9

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The greatest number that appears on both lists is 15.

\n
6. \n
7. The GCF of 27 and 72 is 9.

\n

Decompose 27 and 72 into their prime factors and underline every factor thats common to both:

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27 = 3 x 3 x 3

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72 = 2 x 2 x 2 x 3 x 3

\n

Multiply those underlined numbers to get your answer: 3 x 3 = 9.

\n
8. \n
9. The GCF of 15, 20, and 35 is 5.

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Decompose the three numbers into their prime factors and underline every factor thats common to all three:

\n

15 = 3 x 5

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20 = 2 x 2 x 5

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35 = 5 x 7

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The only factor common to all three numbers is 5.

\n
10. \n
11. The GCF of 44, 56, and 72 is 4.

\n

Decompose all three numbers to their prime factors and underline each factor thats common to all three:

\n

44 = 2 x 2 x 11

\n

56 = 2 x 2 x 2 x 7

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72 = 2 x 2 x 2 x 3 x 3

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Multiply those underlined numbers to get your answer: 2 x 2 = 4.

\n
12. \n
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