Question

a ribbon is 30 inches long and another ribbon is 45 inches long. both ribbons need to be cut into identical pieces, with no ribbon left over. what is the longest length each piece can be?

Explanation:

Step1: Find factors of 30

$30 = 2 \times 3 \times 5$

Step2: Find factors of 45

$45 = 3 \times 3 \times 5$

Step3: Identify common prime factors

Common factors: $3, 5$

Step4: Calculate GCD

$\text{GCD}(30,45) = 3 \times 5 = 15$

Answer:

15 inches