Question

A number when divided by 361 gives a
remainder 47. If the same number is
divided by 19, then the remainder
obtained is
​

Answer 1

Let 'n' be the number

Let q be the quotient on dividing n by 361

Then by Division theorem,

n = 361q + 47

= (19×19)q+(19×2)+9

= 19(19q+2)+9

Let k = 19q+2

⇒n = 19k + 9, 0 ≤ 9 < 19

∴ 9 is there remainder obtained on dividing n by 19