a number when successively divided by 3,5 & 8 leaves remainder 1,4 & 7.what are the respective remainders if the order of divisor be reversed ?

Question

Successive divisors and resp remainders are given.

Answer 1

If I'm understanding your question correctly, the lowest whole number that satisfies this is 238.

238 / 3 = 79 remainder 1

79 / 5 = 15   remainder 4 and

15 / 8 = 1 remainder 7

 

Is this what you mean?

 

The way I got this is working backwards in general. let q be the last quotient.

the dividend then can be represented as 8q + 7.

the dividend before that is 5(8q+7) + 4 = 40q + 39

the dividend before that is 3(40q + 39) + 1= 120q + 118

 

So if q = 1, your original number was 238 as shown

if q = 2, the number would be 358

 

If you reverse the divisors order in either of these 2 numbers, you get a remainder of 6,4,1.

 

Hope this helped