147 Follower Problem

Probability Level 4

a ⋅ b ⋅ c = 147 a < b < c \large a\cdot b\cdot c = 147\ \ \ \ \ a < b < c How many triples of integers ( a , b , c ) (a,b,c) satisfy this equation?

16 9 2 4 10

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Arjen Vreugdenhil by Arjen Vreugdenhil , 44, USA

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1 solution

Arjen Vreugdenhil
Apr 26, 2016

The solutions are

( − 147 , − 1 , + 1 ) ( − 49 , − 3 , + 1 ) ( − 49 , − 1 , + 3 ) ( − 21 , − 7 , + 1 ) ( − 21 , − 1 , + 7 ) ( − 7 , − 3 , + 7 ) ( − 7 , − 1 , + 21 ) ( − 3 , − 1 , + 49 ) ( + 1 , + 3 , + 49 ) ( + 1 , + 7 , + 21 ) \begin{array}{ccccc} (-147, -1, +1) & (-49, -3, +1) & (-49, -1, +3) & (-21, -7, +1) & (-21, -1, +7) \\ (-7, -3, +7) & (-7, -1, +21) & (-3, -1, +49) & (+1, +3, +49) & (+1, +7, +21) \end{array}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

(+7, +3, +7) (-7, -7, 3)?

Siva Bathula - 5 years, 1 month ago

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No-- the problem requires a < b < c a < b < c .

Arjen Vreugdenhil - 5 years, 1 month ago

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Right, I was solving it from my mobile, didn't pay proper attention

Siva Bathula - 5 years, 1 month ago

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