Elementary factorization

Number Theory Level 1

Let d , e , f d, e, f be positive integers such that d ( 10 e + f ) ( 10 f + e ) = 2015 d(10e + f)(10f + e) = 2015 .

Evaluate d × e × f d \times e \times f .


The answer is 15.

Vijay Simha by Vijay Simha , 47, USA

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1 solution

Kay Xspre
Oct 7, 2015

2015 = 5 × 31 × 13 2015 = 5 \times 31 \times 13 . Given that 5, 31 and 13 are relative prime, you can conclude that ( d , e , f ) = ( 5 , 3 , 1 ) , ( 5 , 1 , 3 ) (d, e, f) = (5, 3, 1), (5, 1, 3) Therefore d × e × f = 5 × 3 × 1 = 15 d \times e \times f = 5 \times 3 \times 1 = 15

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