example
Find the greatest common factor of [latex]24[/latex] and [latex]36[/latex].
Solution
Step 1: Factor each coefficient into primes. Write all variables with exponents in expanded form. |
Factor [latex]24[/latex] and [latex]36[/latex]. |
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Step 2: List all factors--matching common factors in a column. |
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In each column, circle the common factors. |
Circle the [latex]2, 2[/latex], and [latex]3[/latex] that are shared by both numbers. |
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Step 3: Bring down the common factors that all expressions share. |
Bring down the [latex]2, 2, 3[/latex] and then multiply. |
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Step 4: Multiply the factors. |
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The GCF of [latex]24[/latex] and [latex]36[/latex] is [latex]12[/latex]. |
Notice that since the GCF is a factor of both numbers, [latex]24[/latex] and [latex]36[/latex] can be written as multiples of [latex]12[/latex].
[latex-display]\begin{array}{c}24=12\cdot 2\\ 36=12\cdot 3\end{array}[/latex-display]
example
Find the greatest common factor of [latex]5x\text{ and }15[/latex].
Answer:
Solution
Factor each number into primes.
Circle the common factors in each column.
Bring down the common factors. |
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The GCF of [latex]5x[/latex] and [latex]15[/latex] is [latex]5[/latex]. |
example
Find the greatest common factor of [latex]12{x}^{2}[/latex] and [latex]18{x}^{3}[/latex].
Answer:
Solution
Factor each coefficient into primes and write
the variables with exponents in expanded form.
Circle the common factors in each column.
Bring down the common factors.
Multiply the factors. |
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The GCF of [latex]12{x}^{2}[/latex] and [latex]18{x}^{3}[/latex] is [latex]6{x}^{2}[/latex] |
example
Find the greatest common factor of [latex]14{x}^{3},8{x}^{2},10x[/latex].
Answer:
Solution
Factor each coefficient into primes and write
the variables with exponents in expanded form.
Circle the common factors in each column.
Bring down the common factors.
Multiply the factors. |
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The GCF of [latex]14{x}^{3}[/latex] and [latex]8{x}^{2}[/latex] and [latex]10x[/latex] is [latex]2x[/latex] |