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1. Decompose the numbers into their prime factors.

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

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5. Multiply the underlined numbers to get the GCF.

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## Sample questions

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

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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

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2 x 3 = 6

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## Practice questions

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

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3. Whats the GCF of 8 and 32?

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5. Find the GCF of 30 and 45.

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7. Figure out the GCF of 27 and 72.

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9. Find the GCF of 15, 20, and 35.

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

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Following are the answers to the practice questions:

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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.

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3. The GCF of 8 and 32 is 8.

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Write down all the factor pairs of 8 and 32:

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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.

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5. The GCF of 30 and 45 is 15.

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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.

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7. The GCF of 27 and 72 is 9.

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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

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

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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:

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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.

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

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

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44 = 2 x 2 x 11

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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.

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