Question

Find the greatest number that will divide 76, 113 and 186 leaving remainders 4, 5 and 6 respectively.

Answer 1

Explanation:

63

445−4=441

572−5=567

699−6=693

⇒ Now, we have to find common factors of 441,567 and 693

441=3×3×7×7

572=3×3×3×3×7

693=3×3×7×11

⇒ The common factors =3×3×7=63

⇒ Here, we can see after dividing 445,572,699 by 63 we get remainder 4,5,6.

∴ The greatest number that will divide 445,572 and 699 leaving remainders 4,5,6 is 63