Question

c. the gcf of an odd number and an even number is always even.

Explanation:

Step1: Analyze the statement

The statement claims "The GCF of an odd number and an even number is always even." Let's test with examples.

Step2: Take an odd and an even number

Let's take the odd number \( 3 \) and the even number \( 6 \). The factors of \( 3 \) are \( 1, 3 \), and the factors of \( 6 \) are \( 1, 2, 3, 6 \). The GCF of \( 3 \) and \( 6 \) is \( 3 \), which is odd.

Step3: Another example

Take odd number \( 5 \) and even number \( 10 \). Factors of \( 5 \): \( 1, 5 \); factors of \( 10 \): \( 1, 2, 5, 10 \). GCF is \( 5 \) (odd).

Step4: Conclusion

Since we found examples where the GCF of an odd and an even number is odd, the statement is false.

Answer:

The statement "The GCF of an odd number and an even number is always even" is false.