How many three digit numbers are divisible by 7?

To do:

We have to find the number of three digit numbers divisible by 7.

Solution:

Let $n$ be the number of terms which are divisible by $7$.

Let $a$ be the first term and $d$ be the common difference.

Multiples of 7 are $7, 14, ....., 98, 105, ....., 994, 1001, ......$

The first three-digit number divisible by $7$ is $105$.

This implies,

$a = 105, d = 7$, last term $a_n = 994$

$a_n = a + (n – 1) d$

$994 = 105 + (n – 1) \times 7$

$994- 105 = 7n – 7$

$7n = 889 +7$

$7n = 896$

$n=\frac{896}{7}$

$n=128$

Therefore, 128 three-digit numbers are divisible by 7.

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

97 Views

Kickstart Your Career

Get certified by completing the course

Get Started