Michelle will divide 36 herbal tea bags and 48 mint tea bags among gift boxes. Each gift box will have the same number of herbal tea bags and the same number of mint tea bags. What is the greatest number of gift boxes Michelle can make?
Factors of 36:
2, 18, 3, 12, 4, 9, 6
Factors of 48
2, 24, 3, 16, 4, 12, 6, 8
What is the greatest common factor of 36 and 48?
To find the greatest number of gift boxes that Michelle can make, we need to find the greatest common divisor (GCD) of the number of herbal tea bags and the number of mint tea bags.
The GCD represents the largest number that divides both 36 and 48 without leaving a remainder.
To find the GCD, we can use the Euclidean algorithm:
1. Divide 48 by 36: 48/36 = 1 with a remainder of 12.
2. Divide 36 by 12: 36/12 = 3 with no remainder.
3. The GCD is the divisor from the previous step, which in this case is 12.
Therefore, the greatest number of gift boxes Michelle can make is 12. Each gift box would contain 3 herbal tea bags and 4 mint tea bags.