What is the greatest number that divides 504, 193 and 231, leaving remainders 4, 13 and 11 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 504 − 4 = 500, 193 − 13 = 180 and 231 − 11 = 220. The greatest number dividing all three is their HCF: 500 = 20 × 25, 180 = 20 × 9, 220 = 20 × 11, and 25, 9, 11 have no common factor, so the HCF is 20. It must also be larger than every remainder, and 20 is.