Question

a number when divided by 143 leaves 31 as remainder. what will be the remainder when the same number is divided by 13 ?

Answer 1

Answer:

Step-by-step explanation:

We know that,

Dividend = divisior x quoitent + remainder.

Given : Divisor = 143.

Remainder = 13.

So, the given no N will be,

N = 143x + 13.

( where x = quotient )

therefore, 143x + 13

➡ 13 ( 11x ) + ( 13 * 2 + 5 )

➡ 13 ( 11x + 2) + 5 ........( taking 13 as common.)

➡ 13 ( 11x + 2 ) + 5

When this no is divided by 13, remainder will be 5.

Answer 2

Answer:

We know that,

Dividend = Divisor × Quotient + Remainder (by Euclid's division lemma)

It is given that:

Divisor = 143

Remainder = 13

So, the given number is in the form of 143x + 31, where x is the quotient.

∴ 143x + 31 = 13 (11x) + (13 × 2) + 5

                    = 13 (11x + 2) + 5  

Thus, the remainder will be 5 when the same number is divided by 13.