Question

Find the greatest number which divides 2011 and 2623, leaving remainders 9 and 5 respectively.

Answer 1

Clearly, we have to find the number which exactly divides (2011 − 9) and (2623 − 5).
So, the required number is the HCF of 2002 and 2618.
$\begin{array}{l}2002\begin{array}{c}1\\ \overline{)\begin{array}{l}\text{2618}\\ \underset{}{-2002}\end{array}}\end{array}\\ \text{616}\overline{)2002}(3\\ \underset{}{-1848}\\ \text{154}\overline{)616}(4\\ -\underset{}{616}\\ \text{0}\end{array}$

∴ The required number is 154.