To find the greatest common factor (GCF) of 40 and 75, we can first find the prime factorizations of both numbers.
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The prime factorization of 40 is: \( 40 = 2^3 \times 5 \)
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The prime factorization of 75 is: \( 75 = 3 \times 5^2 \)
Now, we identify the common factors. Both 40 and 75 share the factor of \( 5 \).
The GCF is the product of the lowest powers of the common prime factors. Here, the only common factor is \( 5^1 \).
Thus, the GCF of 40 and 75 is \( 5 \).
Since 5 is not listed among the response options, it appears there was an oversight in the possible answers provided; none of the answers (A: 22, B: 33, C: 55, D: 7) are correct.
The correct GCF is 5.