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 $89$.