If N is the number of positive integral solutions of the equation x 1 x 2 x 3 x 4 = 770 , then the value of N is

Step-by-step solution

Given, x 1 . x 2 . x 3 . x 4 = 770 = 2.5.7.11 Let positive integer x 1 = 2 a 1 .5 b 1 . 7 c 1 .11 d 1 Let positive integer x 2 = 2 a 2 .5 b 2 .7 c 2 .11 d 2 Let positive integer x 3 = 2 a 3 .5 b 3 .7 c 3 .11 d 3 Let positive integer x 4 = 2 a 4 .5 b 4 .7 c 4 .11 d 4 Now, x 1 x 2 x 3 x 4 = 2 a 1 + a 2 + a 3 + a 4 .5 b 1 + b 2 + b 3 + b 4 .7 c 1 + c 2 + c 3 + c 4 .11 d 1 + d 2 + d 3 + d 4 As per given condition a 1 + a 2 + a 3 + a 4 = 1 , which can be in 4 ways ( 1 , 0 , 0 , 0 ) , ( 0 , 1 , 0 , 0 ) ( 0 , 0 , 1 , 0 )