What is the greatest number that divides 75, 334 and 195, leaving remainders 18, 11 and 5 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 75 − 18 = 57, 334 − 11 = 323 and 195 − 5 = 190. The greatest number dividing all three is their HCF: 57 = 19 × 3, 323 = 19 × 17, 190 = 19 × 10, and 3, 17, 10 have no common factor, so the HCF is 19. It must also be larger than every remainder, and 19 is.