- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- MS Excel
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion Studies
- Legal Studies

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Find the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

Given: 285 and 1249

To find: Here we have to find the value of the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively.

Solution:

If the required number divide 285 and 1249 leaving remainders 9 and 7 respectively, then this means that number will divide 276(285 $-$ 9) and 1242(1249 $-$ 7) completely.

Now, we just have to find the HCF of 276 and 1242.

__Finding HCF of 276 and 1242 using Euclid's division lemma__:

Using Euclid’s lemma to get:

- $1242\ =\ 276\ \times\ 4\ +\ 138$

Now, consider the divisor 276 and the remainder 138, and apply the division lemma to get:

- $276\ =\ 138\ \times\ 2\ +\ 0$

The remainder has become zero, and we cannot proceed any further.

Therefore the HCF of 276 and 1242 is the divisor at this stage, i.e., **138**.

Therefore, the greatest number which divides 285 and 1249 leaving remainders 9 and 7 respectively is 138.