Question

Find the complete remainder when a certain number divided successively by 3, 5 and 7 leaves remainders 2, 3 and 4 respectively? ​

Answer 1

Given :  a certain number divided successively by 3, 5 and 7 leaves remainders 2, 3 and 4 respectively

To find : Remainder when number divided by 5

Solution:

N  = 3A + 2

A = 5B  + 3

B  = 7C  + 4

A  = 5B + 3

=> A = 5(7C + 4) + 3

=> A = 35C + 20 + 3

=> A = 35C + 13

N = 3A  + 2

=> N = 3(35C + 13)  + 2

=> N = 105C + 39 + 2

=> N = 105C  + 41  

N = 105C  + 41  

=> N = 5 (21C) + 40 + 1

=> N = 5(21C + 8) + 1

=> N = 5K + 1

Remainder when Divided by 5  is 1

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