Question

3. A store sells boxes of juice bottles, all the same size. Garth bought 18 bottles, Rico bought 36 bottles, and Mai bought 45 bottles. What is the largest possible number of bottles contained in each box? If each box contains as many bottles as possible, how many boxes did each person buy
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Answer 1

Step-by-step explanation:

we are looking for the greatest common factor of the 3 numbers.

e.g. by prime factorization :

18 = 2×3×3

36 = 2×2×3×3

45 = 3×3×5

the largest chain of prime factor multiplication that is contained in all 3 numbers is 3×3.

the GCF is therefore 3×3 = 9.

and that (9) is the largest possible number of bottles in one box.

oh, and Garth (18 bottles) bought therefore 2 boxes.

Rico (36 bottles) bought 4 boxes.

Mai (45 bottles) bought 5 boxes.