How Many Composite Numbers Are There Between 1 and 200?

Understanding Composite and Prime Numbers

In number theory, a composite number is a natural number greater than 1 that is not prime. A prime number is a number greater than 1 that has exactly two distinct positive divisors: 1 and the number itself.

Step 1: Identifying Prime Numbers Between 1 and 200

First, let's identify the prime numbers within the range of 1 to 200. Here are the prime numbers in this interval:

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199

Step 2: Counting the Prime Numbers

After listing the prime numbers, it's clear that there are 46 prime numbers between 1 and 200.

Step 3: Identifying the Total Numbers Between 1 and 200

The total count of natural numbers from 1 to 200 is 200. This includes all integers in this range, both composite and prime numbers, as well as the number 1.

Step 4: Calculating Composite Numbers

Composite numbers are those that are neither prime nor 1. Therefore, the number of composite numbers can be calculated as follows:

Number of composite numbers Total numbers - Prime numbers - 1

Number of composite numbers 200 - 46 - 1 153

Conclusion

It has been determined that there are 153 composite numbers between 1 and 200. This detailed analysis is crucial for understanding the distribution and characteristics of prime and composite numbers in the given range.

Python 3 Code to Identify Composite Numbers

Here is a simple Python code snippet to list and identify composite numbers within the interval from 1 to 200:

for i in range(2, 201):
    flag  False
    for j in range(2, int(i**0.5)   1):
        if i % j  0:
            flag  True
            break
    if flag  False:
        print(i, "is prime")
    else:
        print(i, "is composite")

This code uses a nested loop to check if a number is divisible by any number between 2 and the square root of the number. If it is not divisible by any such number, it is a prime number; otherwise, it is composite.