Question

A number when successively divided by 1,5 and 8 leaves remainder 1,4 and 7 respectively. Find the respective remainders if the order of divisors be reversed.

Please give step by step formula, correct answer is(6,4,2),I want steps,correct step by step formula will be marked as brainliest and will be rated as 5 stars⭐⭐⭐⭐⭐!!!​

Answer 1

Answer:

Step-by-step explanation:

6, 2, 4

Let us say that a number N, when successively divided by a, b, and c leaves a remainder of p, q, and r

=> Before the last division by c, the number must have been of the format of ck + r. Here k is a natural number.

Same logic can be extended to give the value of N.

=> N = a[b(ck + r) + q] + p

In this case:

N = 3[5(8k + 7) + 4] + 1

=> N = 3[40k + 35 + 4] + 1

=> N = 3[40k + 39] + 1

=> N = 120k + 118

Now, we need to calculate the remainders when the number is successively divided by 8, 3 and 5.

The question will be simpler if I just assume some value of 'k'

Let us put k = 0

=> N = 118

=> 118/8 = 14 + remainder of 6

=> 14/3 = 4 + remainder of 2

=> 4/5 = 0 + remainder of 4

So, the remainders are 6, 2, and 4

Answer 2

Step-by-step explanation:

number when successively divided by 3,5,8 leaving remainders 1,4,7

let as write D=3q+1

Q=5r+1

R=8s+7 substitute 2nd and 3rd eqn in 1st

u will get this eqn 3(5(8k+7)+4)+1,then

=>120k+118

when this number is dived by 8 i.e (120k+118)/8=15k+14 remainder 6

(15k+14)/5=3k+2 remainder 4

(3k+2)/3=k remainder 2

And D) 6,4,2

Hope its clear