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Answer :
To determine the greatest common factor (GCF) of the terms [tex]\(64x^7\)[/tex] and [tex]\(39x^5\)[/tex], we need to follow these steps:
1. Find the GCF of the Coefficients:
- The coefficients of the terms are 64 and 39.
- We need to find the greatest common factor of these two numbers.
- The greatest common factor of 64 and 39 is 1 because there are no common factors other than 1.
2. Find the GCF of the Variables:
- We have the variables [tex]\(x^7\)[/tex] and [tex]\(x^5\)[/tex].
- To find the GCF of the powers of [tex]\(x\)[/tex], we take the smallest power of [tex]\(x\)[/tex] from the given terms.
- The smallest power between 7 and 5 is 5, so the GCF of [tex]\(x^7\)[/tex] and [tex]\(x^5\)[/tex] is [tex]\(x^5\)[/tex].
3. Combine the Results:
- Combine the GCFs of the coefficients and the variables to find the GCF of the terms.
- Since the GCF of the coefficients is 1 and the GCF of the variables is [tex]\(x^5\)[/tex], the overall GCF of the terms is [tex]\(1 \cdot x^5\)[/tex], which simplifies to [tex]\(x^5\)[/tex].
Therefore, the greatest common factor of the terms [tex]\(64x^7\)[/tex] and [tex]\(39x^5\)[/tex] is [tex]\(x^5\)[/tex].
1. Find the GCF of the Coefficients:
- The coefficients of the terms are 64 and 39.
- We need to find the greatest common factor of these two numbers.
- The greatest common factor of 64 and 39 is 1 because there are no common factors other than 1.
2. Find the GCF of the Variables:
- We have the variables [tex]\(x^7\)[/tex] and [tex]\(x^5\)[/tex].
- To find the GCF of the powers of [tex]\(x\)[/tex], we take the smallest power of [tex]\(x\)[/tex] from the given terms.
- The smallest power between 7 and 5 is 5, so the GCF of [tex]\(x^7\)[/tex] and [tex]\(x^5\)[/tex] is [tex]\(x^5\)[/tex].
3. Combine the Results:
- Combine the GCFs of the coefficients and the variables to find the GCF of the terms.
- Since the GCF of the coefficients is 1 and the GCF of the variables is [tex]\(x^5\)[/tex], the overall GCF of the terms is [tex]\(1 \cdot x^5\)[/tex], which simplifies to [tex]\(x^5\)[/tex].
Therefore, the greatest common factor of the terms [tex]\(64x^7\)[/tex] and [tex]\(39x^5\)[/tex] is [tex]\(x^5\)[/tex].
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