To find the greatest common factor (GCF) of the numbers 40 and 75, we can start by finding the prime factorization of each number:
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Prime factorization of 40:
- 40 can be divided by 2: \( 40 \div 2 = 20 \)
- 20 can be divided by 2: \( 20 \div 2 = 10 \)
- 10 can be divided by 2: \( 10 \div 2 = 5 \)
- 5 is a prime number.
So, the prime factorization of 40 is \( 2^3 \times 5 \).
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Prime factorization of 75:
- 75 can be divided by 3: \( 75 \div 3 = 25 \)
- 25 can be divided by 5: \( 25 \div 5 = 5 \)
- 5 is a prime number.
Thus, the prime factorization of 75 is \( 3 \times 5^2 \).
Now, we can find the GCF by looking for the common prime factors:
- The common prime factor is 5.
Now, to determine the GCF:
- The GCF is \( 5^1 = 5 \).
So the greatest common factor (GCF) of 40 and 75 is 5.
Therefore, the answer is: C 5.