Yolo has two pieces of string. One is 32 inches long, and the other is 48 inches long. She wants to make as many necklaces as she can, all of the same length. What is the longest a necklace can be?
What is the greatest common factor of 32 and 48?
16
Is there more information given? If not, there are multiple answers to this problem. Hey, even if she wanted, she could make 80 1-in necklaces (even though it won't fit anyone... xD ) or even 1 80-in necklaces (one size fits all :P ). There has to be some sort of minimum length for the necklace.
The question asks for the longest necklace. You're right, Ashley, the longest will be 16 inches long.
To find the longest possible length for each necklace, we need to determine the greatest common divisor (GCD) of 32 inches and 48 inches. The GCD is the largest number that evenly divides both lengths.
To find the GCD, we can use the Euclidean algorithm:
Step 1: Divide the larger number (48) by the smaller number (32).
48 ÷ 32 = 1 remainder 16
Step 2: Now, divide the smaller number (32) by the remainder (16).
32 ÷ 16 = 2 remainder 0
Step 3: Since we obtained a remainder of 0, the GCD is the last non-zero remainder, which is 16.
Therefore, the longest length for each necklace using the given strings is 16 inches.