- 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 number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

**Given:**

The numbers between 101 and 999.**To do:**

We have to find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

**Solution:**

Numbers that are divisible by 2 and 5 are the multiples of LCM of 2 and 5.

LCM of 2 and 5 $=2\times5=10$

Numbers divisible by 10 are $10, 20,....., 100, 110,....., 990, 1000,......$

Numbers divisible by 2 and 5 between 101 and 999 are $110, 120, ......990$

Here,

First term $a=110$

Common difference $d=10$

Last term $a_n=990$

We know that,

$a_n=a+(n-1)d$

$990=110+(n-1)10$

$990-110=(n-1)10$

$880=(n-1)10$

$88=n-1$

$n=88+1$

$n=89$

**Therefore, the number of natural numbers between 101 and 999 which are divisible by both 2 and 5 is $89$.**

- Related Articles
- Find the sum of all natural numbers between 1 and 100, which are divisible by 3.
- Find the number of numbers which are divisible by $7$ between $100$ and $1000$.
- Find the number of all three digit natural numbers which are divisible by 9.
- Find the sum of all even integers between 101 and 999.
- The number of numbers which are multiples of both 3 and 5 in first 100 natural numbers is____.
- Sum of first N natural numbers which are divisible by 2 and 7 in C++
- A number is divisible by both 5 and 12. By which other number will that number be always divisible?
- Find the least number that is divisible by all the numbers between 1 and 10 (both inclusive).
- Find the sum of all 3-digit natural numbers which are divisible by 13.
- Find the total two-digit numbers which are divisible by $5$.
- Find the sum of all 2-digit natural numbers divisible by 4.
- Find the sum of all natural numbers that are less than 100 and divisible by 4.
- Write the smallest number which is divisible by both 306 and 657.
- Find the smallest number which when increased by 17 is exactly divisible by both 520 and 468.
- Sum of first N natural numbers which are divisible by X or Y

Advertisements