10. Michelle will divide 39 herbal tea bags and 91 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?

How do YOU think you could solve this problem?

hint

find common factor

is it 13?

yes

Yes.

:-)

To find the greatest number of gift boxes that Michelle can make, we need to determine the greatest common divisor (GCD) of 39 (representing the herbal tea bags) and 91 (representing the mint tea bags). The GCD will correspond to the maximum number of gift boxes with the same number of tea bags.

To find the GCD of 39 and 91, we can use a common method called Euclidean algorithm. Here's how it works:

1. Begin by dividing the larger number (91) by the smaller number (39).
- The result is 2, with a remainder of 13: 91 ÷ 39 = 2 remainder 13.

2. Now, divide the previous divisor (39) by the remainder (13).
- The result is 3, with a remainder of 0: 39 ÷ 13 = 3 remainder 0.
- Since the remainder is now 0, we have found the GCD.

Therefore, the greatest common divisor (GCD) of 39 and 91 is 13.

This means that Michelle can make a maximum of 13 gift boxes, with each box containing 13 herbal tea bags and 13 mint tea bags.