Question

A number when divided by 780 gives remainder 38 .What

Answer 1

Given:

A number when divided by 780 gives remainder 38.

To find:

The reminder that would be obtained by dividing same number by 26.

Solution:

According to Euclis' division algorithm,

$a=bq+r$                ...(i)

Where, q is quotient and $0\leq r$ is the remainder.

It is given that a number when divided by 780 gives remainder 38.

Substituting $b=780,\ r=38$ in (i), we get

$a=(780)q+38$

So, given number is in the form of $780q+38$, where q is an integer.

On dividing $780q+38$ by 26, we get

$\dfrac{780q+38}{26}=\dfrac{780q}{26}+\dfrac{38}{26}$

$\dfrac{780q+38}{26}=30q+\dfrac{26+12}{26}$

$\dfrac{780q+38}{26}=30q+\dfrac{26}{26}+\dfrac{12}{26}$

$\dfrac{780q+38}{26}=30q+1+\dfrac{12}{26}$

Since q is an integer, therefore (30q+1) is also an integer but $\dfrac{12}{26}$ is not an integer. Here 26 is divisor and 12 is remainder.

Therefore, the required remainder is 12.