Quantitative Aptitude • Number System & SimplificationHard
What is the greatest number that divides 379, 414 and 171, leaving remainders 1, 8 and 3 respectively?
A. 7
B. 28
C. 14✓ Correct Answer
D. 1
💡 Solution & Explanation
Subtract each remainder first, so the number divides the results exactly: 379 − 1 = 378, 414 − 8 = 406 and 171 − 3 = 168. The greatest number dividing all three is their HCF: 378 = 14 × 27, 406 = 14 × 29, 168 = 14 × 12, and 27, 29, 12 have no common factor, so the HCF is 14. It must also be larger than every remainder, and 14 is.
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