Question

A number when divided by 5,6,7 leaves a remainder 2,5,1 respectively. what is the remainder when divided by 210?

Answer 1

let the number be "n"

number "n" is divided by 5 and leaves remainder 2. hence we can write

n = 5 x + 2                                         eq-1

"x" is now divided by 6 and leaves remainder "5", so we can write

x = 6 y + 5                                             eq-2

"y" is now divided by "7" and leaves remainder "1"

y = 7 z + 1                                              eq-3

using eq-2  and eq-3

x = 6 (7 z + 1) + 5                                  

x = 42 z + 11                                            eq-4

using eq-1 and eq-4

n = 5 (42 z + 11) + 2

n = 210 z + 57

clearly when this number "n" is divided by "210" , the remainder is 57