Question

have.
Emma has 63 comic books, Alex has 49 comic books, and Michael has 77 comic books. Use the GCF and the Distributive Property to find the total number of cosmic books Emma, Alex, and Micheal have.

Answer 1

To find the total number of comic books that Emma, Alex, and Michael have using the greatest common factor (GCF) and the distributive property, we can follow these steps:

1. **Find the GCF of the numbers of comic books:**
- The numbers of comic books are:
- Emma: 63
- Alex: 49
- Michael: 77
- We find the prime factorization of each number:
- \(63 = 3^2 \times 7\)
- \(49 = 7^2\)
- \(77 = 7 \times 11\)

The GCF is the product of the lowest powers of the common prime factors. The only common factor here is \(7\).

2. **Use the GCF to express each number in terms of the GCF:**
- Emma: \(63 = 7 \times 9\)
- Alex: \(49 = 7 \times 7\)
- Michael: \(77 = 7 \times 11\)

3. **Add these expressions using the distributive property:**
- Total number of comic books = \(63 + 49 + 77\)
- This can be rewritten using the GCF:
\[
63 + 49 + 77 = 7 \times 9 + 7 \times 7 + 7 \times 11
\]
- Factor out the GCF (\(7\)):
\[
= 7 \times (9 + 7 + 11)
\]

4. **Calculate the sum inside the parentheses:**
- \(9 + 7 + 11 = 27\)

5. **Multiply by the GCF:**
\[
= 7 \times 27 = 189
\]

Thus, the total number of comic books Emma, Alex, and Michael have is **189**.