Question

Given the sum 100=64+36, rewrite 64+36 using their GCF and multiplication

Answer 1

To rewrite the sum \(64 + 36\) using their greatest common factor (GCF) and multiplication, we first need to determine the GCF of the two numbers.

The prime factorizations of the numbers are:
- \(64 = 2^6\)
- \(36 = 2^2 \times 3^2\)

The common factors between these two numbers involve \(2\). The smallest power of \(2\) common to both factorizations is \(2^2\) (which is \(4\)). Thus, the GCF of \(64\) and \(36\) is \(4\).

Now we can express both \(64\) and \(36\) in terms of their GCF:

- \(64 = 4 \times 16\)
- \(36 = 4 \times 9\)

We can substitute these into the original expression:

\[
64 + 36 = (4 \times 16) + (4 \times 9)
\]

Now, we can factor out the GCF:

\[
64 + 36 = 4 \times 16 + 4 \times 9 = 4 \times (16 + 9)
\]

Calculating \(16 + 9\):

\[
16 + 9 = 25
\]

Thus, we can express \(64 + 36\) as:

\[
64 + 36 = 4 \times 25
\]

Hence, using their GCF and multiplication, we have:

\[
100 = 4 \times 25
\]