Question

How many three digit natural numbers are divisible by 4?

Answer 1

Three-digit natural numbers are 100, 101, 102, 103,…, 997, 998 and 999.
In these numbers, the numbers divisible by 4 are 100, 104, 108,…, 992 and 996.
We observe that these numbers are in an A.P.
Here,
First term, a = 100
Common difference, d = t₂ – t₁ = 104 – 100 = 4
Let the number of these numbers be n.
Thus, we have:
t_n = 996
We know that the n^th term of an A.P. is t_n = a + (n – 1)d.
Thus, we get
996 = 100 + (n – 1)4
$\Rightarrow$996 – 100 = 4(n – 1)
$\Rightarrow$896 = 4(n – 1)
$\Rightarrow$(n – 1) = 224
$\Rightarrow$n = 224 + 1 = 225

Therefore, there are 225 three-digit numbers that are divisible by 4.