Question

Tina has two pieces of ribbon, one 32 inches long and the other 48 inches long. To decorate an album, she wants to cut them up to produce many pieces of ribbon that are all of the same length, with no ribbon left over. What is the greatest length, in inches, that she can make them?

Answer 1

To find the greatest length of ribbon that Tina can cut from both pieces with no ribbon left over, we need to determine the greatest common divisor (GCD) of the two lengths: 32 inches and 48 inches.

We start by listing the factors of each length:

**Factors of 32:**
1, 2, 4, 8, 16, 32

**Factors of 48:**
1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Next, we identify the common factors:
- Both 32 and 48 have the following common factors: 1, 2, 4, 8, 16.

Now, we find the greatest common factor from these:
- The greatest of these common factors is 16.

Thus, the greatest length of ribbon that Tina can cut from both pieces without leaving any leftover is:

\[
\boxed{16} \text{ inches}
\]

To double-check, we can verify the divisibility:
- \(32 \div 16 = 2\) (which is an integer)
- \(48 \div 16 = 3\) (which is also an integer)

Both calculations confirm that 16 is indeed a valid length for cutting the ribbons without leftover. Thus, the answer is correct. The greatest length of ribbon that Tina can make is \( \boxed{16} \) inches.