Question

Find the largest number which divides $70$ and$125$ leaves remainders $5$ and $8$ respectively.

Answer 1

Solve for the HCF of the given numbers

The largest number which divides $70$ and$125$, leaving remainders $5$ and $8$ respectively.

$$\begin{gathered} 70-5=65 \\ 125-5=120 \end{gathered}$$

H.C.F of $65$ and $117$ will be given as,

Factors of $65=1,5,13,65$

Factors of $117=1,3,9,13,39,117$

Common Factors $=1,13$

Highest Common factor $=13$

Hence, the largest number that divides$70$ and$125$, leaving remainders$5$ and $8$, respectively is $13$.