Find the number of numbers between 200 and 300 both included which are...
Counting Numbers
To find the numbers between 200 and 300 (both included) that are not divisible by 2, 3, 4, or 5, we need to follow a systematic approach.
Numbers Divisible by 2
- Every other number is divisible by 2, so we need to exclude half of the total numbers between 200 and 300.
Numbers Divisible by 3
- To find the numbers divisible by 3, we can use the formula for an arithmetic progression: \( \frac{n}{2} \times [a + l] \), where n is the number of terms, a is the first term, and l is the last term.
Numbers Divisible by 4
- Every fourth number is divisible by 4, so we need to exclude those numbers.
Numbers Divisible by 5
- Every fifth number is divisible by 5, so we need to exclude those numbers.
Calculating the Total
- By using the principle of inclusion and exclusion, we can find the total numbers between 200 and 300 that are not divisible by 2, 3, 4, or 5.
By following this systematic approach, you can accurately determine the number of numbers between 200 and 300 (both included) that are not divisible by 2, 3, 4, or 5.