What is the greatest number that divides 239, 181 and 186, leaving remainders 1, 13 and 4 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 239 − 1 = 238, 181 − 13 = 168 and 186 − 4 = 182. The greatest number dividing all three is their HCF: 238 = 14 × 17, 168 = 14 × 12, 182 = 14 × 13, and 17, 12, 13 have no common factor, so the HCF is 14. It must also be larger than every remainder, and 14 is.