What is the greatest number that divides 27, 200 and 131, leaving remainders 6, 4 and 5 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 27 − 6 = 21, 200 − 4 = 196 and 131 − 5 = 126. The greatest number dividing all three is their HCF: 21 = 7 × 3, 196 = 7 × 28, 126 = 7 × 18, and 3, 28, 18 have no common factor, so the HCF is 7. It must also be larger than every remainder, and 7 is.