Question

What is the greatest number that will divide $307$ and $330$ leaving remainders $3$ and $7$ respectively?

• A. $19$
• B. $16$
• C. $17$
• D. $23$

Answer 1

The correct option is A $\left(19\right)$

The concept we use here is: Greatest number with while, when will divide $a,b,c.......$ the remainder are $r_1,r_2,r_3$ respectively
is HCF of $\left[\right(a-r_1\left)\right(a-r_2\left)\right(c-r_3)......]$

Given $1^{st}$ value is $307-3=304$ as remainder $3$

Similar way, $2^{nd}$ value is $330-7=323$ as remainder is $7$

Now, let us find HCF of $304,323$ by division method:

Now H.C.F $304,323$ is $19$

Hence, required greatest number is$19$