There sre 16 rocks that are green and 24 rocks that are blue.
Sharon is dividing her green and blue rock collection into bags. Each bag will contain the same number of each color of rock. How many rocks of each colr will be in each bag?
16 = 2^4
24 = 2^3 3^1
GCF(16,24) = 2^3 = 8
so, there will be 8 bags, each with 2 green and 3 blue rocks
Also there could be
2 bags with 8 green and 12 blue
4 bags with 4 green and 6 blue
To find out how many rocks of each color will be in each bag, we need to determine the greatest common divisor (GCD) of the numbers 16 and 24. The GCD is the largest number that divides evenly into both of the given numbers. Once we find the GCD, we can divide both 16 and 24 by this number to get the desired result.
Step 1: Find the prime factors of each number:
- Prime factors of 16: 2 * 2 * 2 * 2
- Prime factors of 24: 2 * 2 * 2 * 3
Step 2: Determine the common prime factors:
- Both numbers share three 2s as common prime factors.
Step 3: Multiply the common prime factors to find the GCD:
- GCD = 2 * 2 * 2 = 8
Step 4: Divide each number by the GCD:
- 16 ÷ 8 = 2
- 24 ÷ 8 = 3
Therefore, each bag will contain 2 green rocks and 3 blue rocks.