Example
Completion requirements
Example 1
Find the greatest common factor (GCF) of 
.
One method of identifying a GCF is to use prime factorization.
Step 1: Express each term using prime factorization.
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Step 2: Identify all common factors.
Step 3: Determine the product of the common factors. This product will be the GCF.
GCF = 
Step 4: Check the GCF by asking:
- Is 3 the largest factor common to 6, 12, and 15?
- Are exponents on each variable of the GCF the largest permitted given the three terms? Note: the exponents on each variable in the GCF correspond to the lowest exponents on the corresponding variables in the given terms.
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Note that there are no factors common to 
and thus 
is indeed the GCF.
Let's review and compare how the GCF is related to the original expressions.
| Original | Divided by GCF, 3xy2z | Outcome |
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4y |
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5 |
Check:
| Outcome | Multiplied by GCF, 3xy2z (multiplication is the opposite operation of division) | Original |
|---|---|---|
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| 4y | • 4y |
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| 5 | • 5 |
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Performing the reverse operations resulted in exactly what you began with.