What is the greatest number that divides 204, 666 and 419, leaving remainders 6, 6 and 1 respectively?

💡 Solution & Explanation

Subtract each remainder first, so the number divides the results exactly: 204 − 6 = 198, 666 − 6 = 660 and 419 − 1 = 418. The greatest number dividing all three is their HCF: 198 = 22 × 9, 660 = 22 × 30, 418 = 22 × 19, and 9, 30, 19 have no common factor, so the HCF is 22. It must also be larger than every remainder, and 22 is.