2026 · Q24
Let N be the greatest number that will divide 600, 631 and 724, leaving the same remainder. What is the value of N?
Elementary MathematicsHCF and LCM
- A41
- B37
- C33
- D31
Explanation
The required number N must divide the differences of the given numbers, so N divides gcd(631−600, 724−631)=gcd(31,93)=31. Since 31 is prime, N=31, option D. Any integer leaving the same remainder on the three divisions must divide their pairwise differences, which is why the GCD yields the greatest such N.