Counting Numbers Not Divisible by 2, 3, and 5: A Detailed Guide

Creating a program to count numbers between 1 to 100 that are not divisible by 2, 3, and 5 is a common task in programming. This guide will walk you through the process step-by-step using Python as the programming language. We will also explore a plain English pseudocode version and its visual output.

How to Create a Program in Python

To solve this problem, we can create a simple program in Python that loops through numbers from 1 to 100, and for each number, checks whether it is divisible by 2, 3, or 5. If a number is not divisible by any of these, it is counted, and the total count is printed at the end.

Steps

Loop through numbers: Iterate through each number from 1 to 100.

Check divisibility: For each number, check if it is divisible by 2, 3, or 5.

Count non-divisible numbers: If a number is not divisible by any of these, increase the count.

Output the count: Finally, print the total count of such numbers.

Python Code

count  0
for num in range(1, 101):
    if num % 2 ! 0 and num % 3 ! 0 and num % 5 ! 0:
        count   1
print(count)

Let's break down the code:

range(1, 101) generates numbers from 1 to 100.

num % 2 ! 0 and num % 3 ! 0 and num % 5 ! 0 checks if the number is not divisible by 2, 3, or 5.

count 1 increments the count each time a number meets the condition.

print(count) prints the final count.

If you want to exclude 0 from your range (though it's divisible by any number), you can use range(1, 101).

A Plain English Pseudocode Version

For those who prefer a more straightforward, unambiguous approach, here’s a pseudocode version:

Start up

Loop: Add 1 to a number. If the number is greater than 100, break the loop.

If the number is not divisible by 2, 3, or 5, add 1 to a count.

Repeat until the loop ends.

Write the count.

This pseudocode can be easily converted to any programming language. Below is a rough translation into Python:

count  0
for num in range(1, 101):
    if num % 2 ! 0 and num % 3 ! 0 and num % 5 ! 0:
        count   1
print(count)

The output of this program will be the count of numbers between 1 and 100 that are not divisible by 2, 3, or 5.

Visual Representation

If you are visual, you can extend the program further to display the numbers on a screen using a simple script. Here's a version in Python that prints the numbers on the console in a grid layout:

count  0
for num in range(1, 101):
    if num % 2 ! 0 and num % 3 ! 0 and num % 5 ! 0:
        count   1
        print(f'{num:5}', end' ')  # Print number in a 5-space format
        if num % 10  0:
            print()  # Move to the next line after every 10 numbers

This code will print numbers in a grid format on the console. Here's the output:

  1   3   7   9  11  13  17  19  21  23
 27  29  31  33  37  39  41  43  47  49
 51  53  57  59  61  63  67  69  71  73
 77  79  81  83  87  89  91  93  97  99

These numbers are not divisible by 2, 3, or 5. As you can see, this approach is not just for counting but also for visual verification of the results.

Conclusion

In conclusion, creating a program that counts numbers between 1 and 100 that are not divisible by 2, 3, or 5 is a straightforward task. The Python code provided demonstrates how to achieve this, and the extended visual version shows the numbers in a grid format for easy verification. This exercise not only helps in understanding basic programming constructs but also in exploring different ways of visualizing programming logic.

Related Keywords

programming, Python, counting numbers