What is the greatest number that divides 414, 339 and 377, leaving remainders 6, 16 and 3 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 414 − 6 = 408, 339 − 16 = 323 and 377 − 3 = 374. The greatest number dividing all three is their HCF: 408 = 17 × 24, 323 = 17 × 19, 374 = 17 × 22, and 24, 19, 22 have no common factor, so the HCF is 17. It must also be larger than every remainder, and 17 is.