Question

Complete the following statements with suitable words or figures.

I am a number between $10$ and $20$. If you divide $100$ or $122$ by me, the remainder is $1$. I am the number…………

Answer 1

Step $1$: Subtract $1$ from both the numbers.

So, the numbers are $(100-1=99)$ and $(122-1=121)$

Step $2$: Find the prime factorisation of $99$ and $121$

$$\begin{gathered} 99=3\times 3\times 11 \\ 121=11\times 11 \end{gathered}$$

The H.C.F. of the numbers is $11$

Hence, the answer is $11$