7. How many three digit natural numbers are divisible by 4 ?


7. How many three digit natural numbers are divisible by 4 ? 

Sol. The three digit natural numbers that are divisible by 4 are : 100, 104, 108, ........ 996.

It is an A.P. with a = t1 = 100, d = 4

Let, tn = 996

We know that for an A.P.

tn = a + (n – 1) d

 996 = 100 + (n – 1) 4
 996 = 100 + 4n – 4
 996 = 96 + 4n
 4n = 996 – 96
 4n = 900
 n = 900/4
 n = 225


 There are 225 three digit natural numbers that are divisible by 4.