Question

Find the greatest number that will divide $43,91$ and $183$ so as to leave the same remainder in each case.

• A. $4$
• B. $7$
• C. $9$
• D. $13$

Answer 1

The correct option is A $4$

Here, we need to find differences between the given numbers. If two numbers give the same remainder when divided by some other number, then their difference must give a remainder of zero when divided by that number.
Our numbers here are $91-43=48,183-91=92,183-43=140$
So we have the set of numbers $\{48,92,140\}$ and we want to know the biggest number that divides all these numbers.

So,

$48=2\times 2\times 2\times 3$

$92=2\times 2\times 23$

$140=2\times 2\times 5\times 7$

The greatest common divisor of $\{48,92,140\}$ is $4.$

So, answer is $4.$