Answer:
B. 4 bags
Step-by-step explanation:
The number of bags that will have the same quantities of the different gifts is the Greatest Common Divisor of the numbers of gifts.
GCD(24, 32, 44) = 4
Mrs. Dupree can make at most 4 identical bags.
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<em>How to find the GCD</em>
The GCD can be found by looking at factors:
- 24 = 4·6
- 32 = 4·8
- 44 = 4·11
4 is the largest common factor of these numbers.
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The GCD can also be found using Euclid's algorithm. In that algorithm, the larger number is divided by the smaller, with the remainder replacing the larger number after each step. If the remainder is zero, the smaller number is the GCD.
The GCD of several numbers can be found by finding the GCD of a pair, then of that value and the next number:
GCD(24, 32, 44) = GCD(GCD(24, 32), 44) = GCD(8, 44) = 4
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32/24 = 1 r 8 . . . . first step in Euclid's algorithm for GCD(24, 32)
24/8 = 3 r 0 ⇒ GCD(24, 32) = 8
Then
44/8 = 5 r 4
8/4 = 2 r 0 ⇒ GCD(8, 44) = 4 = GCD(24, 32, 44)
