Sarah has 24 blue beads, 36 gold beads, 60 silver beads, and 72 purple beads. She is planning to decorate jewelry boxes for her friends and wants to distribute the beads evenly among the jewelry boxes. What is the greatest number of jewelry boxes that Eva can make?
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To find the greatest number of jewelry boxes that Sarah can make while distributing the beads evenly, we need to find the greatest common divisor (GCD) of the total number of beads.
First, let's find the total number of beads:
Total number of beads = 24 (blue beads) + 36 (gold beads) + 60 (silver beads) + 72 (purple beads)
Total number of beads = 192 beads
Now, we need to find the GCD of the total number of beads, which will give us the maximum number of jewelry boxes that she can make. We can use the Euclidean algorithm to find the GCD.
To find the GCD, we divide the largest number (192) by the smallest number (24) and find the remainder.
192 รท 24 = 8 with a remainder of 0
Since the remainder is 0, 24 is the GCD. This means that Sarah can make a maximum of 24 jewelry boxes with an even distribution of the beads.
Therefore, the greatest number of jewelry boxes Sarah can make is 24.