Question

How many natural numbers less than 300 are there which are neitherdivisible by 5 nor by 7?​

Answer 1

Given: Natural numbers less than 300.

To find: Natural numbers neither divisible by 5 nor by 7.

Solution:

• Natural numbers include 1, 2, 3, 4, and so on.
• To check for numbers that are divisible by both 5 and 7, we first multiply 5 and 7,

        $5 * 7 = 35$.

• Then, we divide 300 by 5,

        $\frac{300}{35} = 8.57$.

• 300 divided by 35 will give 8 as quotient and 20 as remainder.
• So there are 8 numbers less than 300 that are divisible both by 5 and 7.
• To find the numbers that are divisible neither by 5 nor by 7, we deduct 8 from 300,

        $300 - 8 = 292$.

Therefore, there are 292 natural numbers less than 300 that are divisible neither by 5 nor by 7.