1.1 Prep Exercise: Greatest Common Factor
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Finding the GCF |
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Greatest common factor. Think about those three words. Greatest. Common. Factor. What is the greatest factor common to all expressions? |
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Example 1. Find the greatest common factor of 12 and 15. |
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Write each number in factored form |
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Take each factor common to both, the number of times in common. The greatest factor common to 12 and 15 is 3. |
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The GCF is 3. |
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Example 2. Find the greatest common factor of 20 and 30. |
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Write each number in factored form: |
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Take each factor common to both, the number of times in common. |
Both 20 and 30 contain the factors 2 and 5 (each one time). |
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The GCF
is |
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What operation holds two factors together? |
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Given one factor of 30, say 6, how do you find the other factor? |
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Example 3. Find the GCF of |
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Write each expression in factored form. |
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The variable x is common to both three times. |
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The GCF is |
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Compare your answers to the checkpoint problems with a colleague, then discuss any pattern you have found. Given two variable terms with the same variable but different powers, which of the two is the GCF, the lower power or the higher? Explain. |
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In
symbols, suppose you are given |
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When given any number of terms with the same variable to different powers, the GCF is the term with the lowest exponent.