Answer :

reishumwi
The largest number which divides 85 and 77, leaving remainders 5 and 7 respectively = The H.C.F of (85 - 5) and (77 - 7)
                  = The H.C.F of 80 and 70.
(By prime factor method)
Since, 80 = 2 × 2 × 2 × 2 × 5
   and, 70 = 2 × 5 × 7
H.C.F of 80 and 70 = Product of common prime factors
                           = 2 × 5 = 10
Therefore, the largest number which divides 85 and 77, leaving remainders 5 and 7 respectively = 10

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Mathexpert
We need to find the largest number which divides 85 and 77, leaving remainders 5 and 7 respectively.
Consider the numbers (85 - 5 = 80) and (77 - 7 = 70)
The HCF of 80 and 70 is 10

The largest number which divides 85 and 77, leaving remainders 5 and 7 respectively is 10

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