Marcus Collects donations and care packages for troops overseas He has 36 bars of soap and 24 toothbrushes and wants to arrange the packages so they are identical. What is the greatest number of packages Marcus can make using all the Soap and toothbrushes?

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
7 days ago

To find the greatest number of identical packages Marcus can make using all of the 36 bars of soap and 24 toothbrushes, we need to determine the greatest common divisor (GCD) of the two numbers.

1. **Find the factors of each number:**
- For 36: The factors are 1, 2, 3, 4, 6, 9, 12, 18, 36.
- For 24: The factors are 1, 2, 3, 4, 6, 8, 12, 24.

2. **Identify the common factors:**
- The common factors of 36 and 24 are 1, 2, 3, 4, 6, and 12.

3. **Determine the greatest common factor:**
- The greatest common factor is 12.

Thus, the greatest number of identical packages that Marcus can make using all of the soap and toothbrushes is **12** packages.

In each package, he would include:
- \( \frac{36 \text{ bars of soap}}{12 \text{ packages}} = 3 \text{ bars of soap per package} \)
- \( \frac{24 \text{ toothbrushes}}{12 \text{ packages}} = 2 \text{ toothbrushes per package} \)

So, each of the 12 packages would contain 3 bars of soap and 2 toothbrushes.