Problem 21 · 2017 Math Kangaroo
Stretch
Number Theory
factorizationfactor-pairs
In the primate enclosure in a zoo there are four gorillas. They are all younger than 18 years old. No two have the same age, and all their ages are whole numbers. The product of their ages is 882. How big is the sum of their ages?
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Answer: D — 31
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Hint 1 of 2
Factor 882 and split it into four different whole numbers, all under 18.
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Hint 2 of 2
Use the prime factorisation 882 = 2 · 3² · 7².
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Approach: factor 882 into four distinct factors below 18
- 882 = 2 · 3² · 7².
- The only way to write it as four distinct factors each under 18 is 1 · 7 · 9 · 14 = 882.
- Their sum is 1 + 7 + 9 + 14 = 31, choice D.
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