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

Answer
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Hint: Subtract the remainders i.e. 4 and 3 from the given numbers i.e. 280 and 1245 and then calculate H.C.F of those numbers. That HCF will be our required answer.

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 $2 \times 3 \times 23 = 138$
So, the largest number which exactly divides 280 and 1245 leaving remainders 4 and 3 respectively is 138.

Note: The HCF or Highest common factor of two or more given numbers is the largest number which divides each of the given numbers without leaving any remainder. The LCM or Least common factor of two or more numbers is the smallest of the common multiples of those numbers.