Find the greatest number which divides 2011 and 2623 leaving remainder 9 and 5 respectively.?

Question

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

Answer

154

Answer

Problem Statement

Find the greatest number that divides 2011 and 2623, leaving remainders of 9 and 5 respectively.

Solution

To find the greatest number that divides two given numbers, we need to find their common factors. By finding the common factors, we can determine the greatest number that divides both numbers.

Step 1: Finding Factors of 2011

To find the factors of 2011, we can start by checking for numbers less than or equal to the square root of 2011. If a number divides 2011 without leaving a remainder, it is a factor of 2011.

Factors of 2011: 1, 2011

Step 2: Finding Factors of 2623

Similarly, we can find the factors of 2623 by checking for numbers less than or equal to the square root of 2623.

Factors of 2623: 1, 17, 154, 289, 2623

Step 3: Finding Common Factors

Now, let's find the common factors of 2011 and 2623.

Common factors: 1

Step 4: Finding the Greatest Common Factor

Since the greatest common factor is the largest number that divides both 2011 and 2623, we conclude that the greatest number is 1.

Explanation

When two numbers have a common factor, it means that they share a divisor. In this case, the given numbers 2011 and 2623 have a common factor of 1.

Any number greater than 1 would result in a remainder when dividing both 2011 and 2623. Therefore, the greatest number that divides 2011 and 2623, leaving remainders of 9 and 5 respectively, is 1.

Summary

- The factors of 2011 are 1 and 2011.
- The factors of 2623 are 1, 17, 154, 289, and 2623.
- The common factor of 2011 and 2623 is 1.
- The greatest number that divides both 2011 and 2623, leaving remainders of 9 and 5 respectively, is 1.

Answer

Hcf of 2002

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