Question

Find the largest two-digit number that divides $673$ and $865$ leaves the remainder $1$ in each.

Answer 1

Solve for the HCF to get the required number,

Finding factors for the first number,

$673-1=672$ (As the remainder is $1$.)

Factorize $672$

$\Rightarrow 672=2\times 2\times 2\times 2\times 2\times 3\times 7$

Finding factors for the second number,

$865-1=864$(Remainder is $1$)

Factorize $864$

$\Rightarrow 864=2\times 2\times 2\times 2\times 2\times 3\times 3\times 3$

The HCF of $672$ and $864$ is

$$\begin{gathered} HCF(672,864)=2\times 2\times 2\times 2\times 2\times 3 \\ \Rightarrow HCF(672,864)=96 \end{gathered}$$

Hence, the largest two-digit number that divides $673$ and $865$ by leaving the remainder $1$ in each is $96$.