Question

Find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3, respectively.

Answer 1

From the question it’s understood that, 

280 – 4 = 276 and 1245 – 3 = 1242 has to be exactly divisible by the number. 

Thus, the required number should be the H.C.F. of 276 and 1242. 

Now, applying Euclid’s division lemma 

1242 = 276 x 4 + 138 

276 = 138 x 2 + 0 (the remainder becomes 0 here) 

And hence the H.C.F (280, 1245) = 138 

∴ The required number is 138.