Question

Find the greatest number which divides 2011 and 2623 leaving remainders 9 and 5 respectively

Answer 1

Answer:

The greatest number obtained here is 154.  

Solution:

Let the greatest number to find be a.

When 2011 is divided by a, remainder left = 9.

Thus, (2011-9) is divisible by a.

Hence, 2002 is divisible by a.

And, When 2623 is divided by a, remainder left = 5.

Thus, (2623-5) is divisible by a.

Therefore, 2618 is divisible by a.

Now to find a, we need to find out the "Highest Common Factor" or "H.C.F." of "2002 and 2618".

So, "H.C.F." of "2002 and 2618" is 154.

Hence, the greatest number is 154.

Answer 2

Greatest number, which divides both 2011 and 2623 is 154

Solution:

Greatest number be denoted as a.

When 2011 is divided by a

Remainder of division = 9.  

Value (2011-9) can be divided by a.

Number 2002 is divisible by a.

When 2623 is divided by a

Remainder of division =  5.

Value (2623 – 5) can be divided by a.  

Number 2618 is again divisible by a.

HCF of 2002 and 2618 = 154 (can be found out by factorizing each number or long division method)