Problem 6 · 2009 Math Kangaroo
Easy
Number Theory
factorizationfactor-pairs
The product of four different natural numbers is 100. What is the sum of the four numbers?
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Answer: D — 18
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Hint 1 of 2
Write 100 as a product of four DIFFERENT whole numbers - the smallest will be 1.
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Hint 2 of 2
100 = 2^2 x 5^2; split those primes into four distinct factors.
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Approach: factor 100 into four distinct numbers
- 100 = 2^2 x 5^2. Using four different factors forces 1, 2, 5 and 10 (since 1x2x5x10 = 100).
- No other set of four distinct naturals multiplies to 100.
- Their sum is 1+2+5+10 = 18.
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