Tisha has 20 glasses and 15 mugs. She would like to set them out in identical groups, with none left over, in preparation for a dinner party. What is the greatest number of groups Tisha can set out?
Question
Tisha has 20 glasses and 15 mugs. She would like to set them out in identical groups, with none left over, in preparation for a dinner party. What is the greatest number of groups Tisha can set out?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of glasses and mugs. The GCD is the largest number that divides both numbers without leaving a remainder.
Step 1: Identify the numbers. Here, the numbers are 20 (glasses) and 15 (mugs).
Step 2: Find the GCD of 20 and 15.
The factors of 20 are: 1, 2, 4, 5, 10, 20. The factors of 15 are: 1, 3, 5, 15.
The common factors are: 1 and 5.
Step 3: Identify the greatest common factor. Here, the GCD is 5.
So, Tisha can set out the glasses and mugs in 5 identical groups with none left over.
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