Question

A number when divided by 627 leaves a remainder 43. by dividing the same number by 19, the remainder will be?

Answer 1

It will be 5.below is the explanation

Answer 2

The remainder will be 5

Step-by-step explanation:

We know that dividend = divisor $\times$ quotient + remainder

Let the dividend number required be x.

When x is divided by 627, the remainder is 43.

x = 627k + 43

Where,

k is the quotient

627 is the divisor

43 is remainder.

Here, x is the multiple of 627

Let us consider the factors of 627

$627 = 3 \times 209 = 3 \times 19 \times 11$

Expressing the equation in terms of 19 would help to solve the problem, as we need to find the remainder when x is divided by 19.

As 43 = 38 + 5 = 19 $\times$ 2 + 5

Therefore,

$x = 19 \times 3 \times 11 \times k + (19 \times 2 + 5)$

x = 19(33k + 2) + 5

This is in the form of dividend, divisor, quotient, and remainder.

This means that x when divided by 19 with divisor 33k + 2, gives remainder 5.

Therefore, the remainder is 5 when the same number is divided by 19.