Question

A number when successfully divided by 3,5,8 leaves remainder 1,4,7 . Find the respective remainders if the orders of divisors be reversed

Answer 1

Answer:

6, 4, 2     ....     if the problem means what I think it means :-)

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Step-by-step explanation:

"successively"?  If so...

I think the problem means this:

1) a divided by 3 is b with remainder 1

2) b divided by 5 is c with remainder 4

3) c divided by 8 is d with remainder 7

Same process but with divisors 8, 5 then 3, what would be the remainders?

1) => a = 3b + 1

2) => b = 5c + 4 => a = 3(5c+4) + 1 = 15c + 13

3) => c = 8d + 7 => a = 15( 8d + 7 ) + 13 = 120d + 118

Now to process:

1*) a = (8)(15)d + (8)(14) + 6 = 8 ( 15d + 14 ) + 6

                                 --> remainder 6 when divide by 8

2*) 15d + 14 = (5)(3d) + (5)(2) + 4 = 5 ( 3d + 2 ) + 4

                                 --> remainder 4 when divide by 5

3*)  3d+2  -->  remainder 2 when divide by 3