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

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**Complete step by step answer:**

To find the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively, so, we subtract 4 and 3 from 280 and 1245.

$ 280 - 4 = 276$

$ 1245 - 3 = 1242 $

Now calculate the factors of 276 and 1242

$ 276 = 2 \times 2 \times 3 \times 23 $

$ 1242 = 2 \times 3 \times 3 \times 3 \times 23 $

Now calculate the H.C.F of 276 and 1242

As we know H.C.F of any two numbers is the common factor of the numbers.

Therefore the common factors of 276 and 1242 is $2 \times 3 \times 23 = 138$