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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 $89$.