Question 1013776: A relief worker needs to divide 240 bottles of water and 144 cans of food into groups that each contain the same number of items. Also, each group must contain the same type of item (bottled water or csnned food). What is the largest number of relief supplies that can be put into each group?
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Found 2 solutions by mathmate, josmiceli:
Answer by mathmate(429)   (Show Source):
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Question:
A relief worker needs to divide 240 bottles of water and 144 cans of food into groups that each contain the same number of items. Also, each group must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put into each group?
Solution:
This problem is related to HCF (highest common factor).
The maximum number of groups is the HCF of 240 and 144.
The number of items in each group is 240 or 144 divided by the HCF.
To find the HCF of two numbers, we can either factor each number into powers of primes, and determine the maximum power of each prime factor that is common to both numbers, as follows:
Hence the HCF is 
We calculate 240/48=5, 144/48=3,
So there can be a maximum of 48 groups, with 5 bottled water and 3 canned food.
Alternatively, we can find the HCF by the Euclid algorithm, which is taking the difference between the remainder of the large number divided by the small number, until the difference is 0.
240-144*1=96
144-96*1=48
96-48*1=48
48-48*1=0
so the HCF is 48.
Answer by josmiceli(19441)  (Show Source):
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