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?
Please help,
What is the highest common factor of 24, 36, 60, and 72 ?
24 = 2*2*2*3
36 = 2*2*3*3
60 = 2*2*3*5
72 = 2*2*2*3*3
So the LCF is 2*2*3 = 12
( we should have been able to see that mentally given the nice numbers)
So she can make 12 boxes, each with 2 blues, 3 gold, 5 silver and 6 purple beads
U HAVE A GREAT YEAR OUUU AH BUM BUM BUN NA BUM BUM BUM DOH DA
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 given quantities of beads. The GCD represents the largest possible number of boxes that can be made with an equal distribution of beads.
To find the GCD, we can use a few different methods. One common method is using prime factorization. Another method is using the Euclidean algorithm.
Let's use the prime factorization method to find the GCD:
1. Prime factorize each quantity of beads:
- 24 blue beads: 2 * 2 * 2 * 3 = 2^3 * 3
- 36 gold beads: 2 * 2 * 3 * 3 = 2^2 * 3^2
- 60 silver beads: 2 * 2 * 3 * 5 = 2^2 * 3 * 5
- 72 purple beads: 2 * 2 * 2 * 3 * 3 = 2^3 * 3^2
2. Identify the common prime factors.
- The common prime factors are 2^2 * 3 = 12.
3. Multiply the common prime factors to find the GCD.
- GCD = 2^2 * 3 = 12
Therefore, the greatest number of jewelry boxes that Sarah can make with an equal distribution of beads is 12.