Question

Find the greatest number that divides 582 and 680 leaving remainders 6 and
4 respectively.
​

Answer 1

4 is the greatest number.

Since on dividing 582 by the required number, the remainder is 6. Therefore, 582−6 = 576 will be exactly divisible by the required number.

Similarly, 680−4 = 676 will be also exactly divisible by the required number.

Therefore, the required number is the HCF of 576 and 676.

Let us do the prime factorization of 576 and 676 to find the HCF:

576 = 2×2×2×2×2×2×3×3

676 = 2×2×13×13

⇒HCF( 576 , 676 ) = 2×2 = 4

Hence, 4 is the largest number which divides 582 and 680 leaving remainders 6 and 4.

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