B has 32 pens , 24 pencils and 16 erasers .How many sets of these three items can B make without any left over ?
A. 6
B. 7
C. 8
D. 9

Options

A. A
B. D
C. B
D. C

Answer

To determine how many sets of pens, pencils, and erasers B can make without any leftover, we need to find the greatest common divisor (GCD) of the quantities of each item.

### Step-by-Step Solution:

1. **Identify the quantities of each item:**
- Pens: 32
- Pencils: 24
- Erasers: 16

2. **Find the GCD of the quantities:**
- We will find the GCD of 32, 24, and 16.
- First, we can find the prime factorization of each number:
- 32 = 2^5
- 24 = 2^3 × 3^1
- 16 = 2^4

3. **Identify the common prime factors:**
- The common prime factor among these numbers is 2.
- The lowest power of 2 in the factorizations is 2^3 (from 24).

4. **Calculate the GCD:**
- Thus, GCD(32, 24, 16) = 2^3 = 8.

5. **Determine the number of sets:**
- The GCD tells us how many complete sets can be made without any leftover.
- Therefore, B can make **8 sets** of pens, pencils, and erasers.

### Final Answer:
B can make **8 sets** of these three items without any leftover. The answer is **C. 8**.