Glenn wants to pack 56 erasers and 70 rulers into as many bags as possible, with no remainder. The total number of erasers and rulers was the same in each bag. The number of erasers in each bag was the same. How many erasers were there in each bag?
Question
Glenn wants to pack 56 erasers and 70 rulers into as many bags as possible, with no remainder. The total number of erasers and rulers was the same in each bag. The number of erasers in each bag was the same. How many erasers were there in each bag?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of 56 and 70, which is the largest number that can divide both numbers without a remainder.
Step 1: List the divisors of each number. The divisors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56. The divisors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70.
Step 2: Find the greatest number that appears in both lists. The greatest common divisor of 56 and 70 is 14.
Step 3: Divide the total number of erasers by the GCD. 56 erasers ÷ 14 = 4 erasers.
So, there were 4 erasers in each bag.
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