The product of a three digit number and the number obtained by reversing the is 83187.Find the three digit number
Answers
Given : The product of a three digit number and the number obtained by reversing the is 83187
To Find : 3 digit number
Solution:
3 digit number = abc
number obtained by reversing the digits = bca
c * a end with 7
only possible if 1 * 7 = 7 or 3 * 9 = 27
case 1 :
a = 1 and c = 7
=> 1b7 * 7b1 = 83187
=> (107 + 10b) (701 + 10b) = 83187
=> 75007 + 100b² + 10b(808) = 83187
=> 100b² + 10b(808) - 8180 = 0
=> 10b² + 808b - 818 = 0
=> 10b² + 818b - 10b - 818 = 0
=> 10b(b - 1) + 818(b - 1) = 0
=> b = 1
Hence 117 and 711 are the number
117 * 711 = 83187
case 2 :
a = 3 and c = 9
=> 3b9 * 9b3 = 83187
=> (309 + 10b) (903 + 10b) = 83187
309 * 903 > 83187 Hence not possible
So 117 and 711 are the required 3 digit number
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