Question

Which correctly shows how to use the GCF and the distributive property to find an expression equivalent to 24 + 44?
4 (6 + 11)
2 (12 + 22)
6 (4 + 11)
2 (12 + 6)

Answer 1

To find an expression equivalent to \(24 + 44\) using the greatest common factor (GCF) and the distributive property, we first need to determine the GCF of the two numbers.

1. **Find the GCF**:
- The prime factorization of \(24\) is \(2^3 \times 3\).
- The prime factorization of \(44\) is \(2^2 \times 11\).
- The GCF of \(24\) and \(44\) is \(4\) (since \(2^2\) is the highest power of \(2\) they share).

2. **Factor out the GCF**:
- We can write \(24\) as \(4 \times 6\) and \(44\) as \(4 \times 11\).
- Therefore, we can express \(24 + 44\) as:
\[
24 + 44 = 4 \times 6 + 4 \times 11
\]
- Now using the distributive property, we can factor out the \(4\):
\[
4 \times 6 + 4 \times 11 = 4(6 + 11)
\]

Thus, the expression \(24 + 44\) can be rewritten as \(4(6 + 11)\).

Therefore, the correct choice is:

**4 (6 + 11)**.