Question

a number being successively divided by 1,4and7 leaves remainders 3,5 and 7 respectively. find the respective remanders if the order of divisors be reversed

Answer 1

Answer:

Let the number(dividend) be D, and the quotients obtained after the successive divisions be q, r, & s respectively.

Writing the given data mathematically using Dividend = Divisor * Quotient + Remainder, we get

D = 3q + 1

q = 5r + 4

r = 8s + 7

Passing value of r in q, & then value of q in D, we get

D = 3[5(8s + 7) + 4] + 1

=> D = 3(40s + 39) + 1

=> D = 120s + 118, where s can be any whole number.

Successively dividing D by 8, 5, and 3 (reversing the previous order), we get

D/8 = (120s + 118)/8, which gives quotient = (15s + 14) & remainder = 6

Then, (15s + 14)/5 gives quotient = (3s + 2) & remainder = 4

Finally, (3s + 2)/3 gives quotient = s & remainder = 2

Therefore, the respective remainders are 6, 4, 2.

Step-by-step explanation:

Hope it helps