What is the greatest number that divides 212, 243 and 377, leaving remainders 12, 18 and 2 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 212 − 12 = 200, 243 − 18 = 225 and 377 − 2 = 375. The greatest number dividing all three is their HCF: 200 = 25 × 8, 225 = 25 × 9, 375 = 25 × 15, and 8, 9, 15 have no common factor, so the HCF is 25. It must also be larger than every remainder, and 25 is.