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.