Question

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

Hint: - Subtract the remainders from the numbers and then calculate H.C.F of the numbers.

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 $2 \times 3 \times 23 = 128$
So, the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively is 128.

Note: - In such types of questions first subtract the remainder from the given numbers, then calculate the H.C.F of the numbers which we get after subtracting, H.C.F is the required largest number which exactly divides the given number leaving remainder 4 and 3 respectively.