Problem 7 · 2018 Math Kangaroo
Hard
Number Theory
factorizationdivisibility
Maria wants to share 42 apples, 60 peaches and 90 cherries fairly. She puts them into baskets that each hold the same number of apples, the same number of peaches and the same number of cherries, and gives one basket to each friend. At most, how many baskets can she fill?
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Answer: B — 6
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Hint 1 of 2
The number of baskets must divide each of 42, 60 and 90 exactly.
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Hint 2 of 2
Find the greatest common divisor of 42, 60 and 90.
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Approach: greatest common divisor
- Each fruit count must split evenly among the baskets, so the number of baskets divides 42, 60 and 90.
- The largest such number is gcd(42, 60, 90) = 6.
- So she can fill at most 6 baskets.
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