QuestionDecember 16, 2025

The GCF of 40c^6 and 48c^7 is 8c The missing exponent is __ The solution is square

The GCF of 40c^6 and 48c^7 is 8c The missing exponent is __ The solution is square
The GCF of 40c^6 and 48c^7 is 8c
The missing exponent is __
The solution is square

Solution
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Answer

6 Explanation 1. Find numerical GCF Prime factors: 40 = 2^3 \cdot 5, 48 = 2^4 \cdot 3. Numerical GCF = 2^3 = 8. 2. Find variable GCF For c: exponents are 6 and 7. GCF exponent = \min(6,7) = 6. So GCF variable part = c^6. 3. Compare with given GCF Given GCF is 8c^x, so c^x = c^6. Thus x = 6.

Explanation

1. Find numerical GCF <br /> Prime factors: $40 = 2^3 \cdot 5$, $48 = 2^4 \cdot 3$. Numerical GCF = $2^3 = 8$. <br />2. Find variable GCF <br /> For $c$: exponents are $6$ and $7$. GCF exponent = $\min(6,7) = 6$. So GCF variable part = $c^6$. <br />3. Compare with given GCF <br /> Given GCF is $8c^x$, so $c^x = c^6$. Thus $x = 6$.
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