Python Simple Programs (using while loop) – Part 3
🔢 1. Compute Factorial of N
➜ This Python program calculates the factorial of a number using a while loop.
✨ Factorial Concept
N! = N × (N − 1) × … × 2 × 1
For example:
5! = 5 × 4 × 3 × 2 × 1 = 120
💡 How It Works
1.
The user enters the value of N.
2.
factorial starts with 1 and
i starts with 1.
3.
The while loop continues as long as
i <= n.
4.
Each value of i is multiplied with
factorial.
5.
i = i + 1 moves the counter to the next value.
6.
When i > n, the loop stops and the factorial is displayed.
🔎 Step-by-Step: N = 5
factorial = 1 × 1 = 1
factorial = 1 × 2 = 2
factorial = 2 × 3 = 6
factorial = 6 × 4 = 24
factorial = 24 × 5 = 120
⚠️ Important: Updating the Counter
Unlike a for loop, a while loop
does not automatically update the counter.
i = i + 1
This statement is necessary to move toward the loop’s stopping
condition. Without it, the loop could continue indefinitely.
▶ Sample Output
Enter value of N: 5
Factorial of N is: 120
📌 Quick Note:
A while loop is useful when the number of repetitions
depends on a condition. Always make sure that the loop condition can
eventually become False.
➕ 2. Sum of First Five Natural Numbers
➜ This Python program uses a while loop to calculate the sum of the first five natural numbers.
▶ Sample Output
Sum of 1st 5 numbers is: 15
💡 How It Works
1.
sum is initialized to 0.
2.
count starts at 1.
3.
The while loop runs while
count <= 5.
4.
Each value of count is added to sum.
5.
count = count + 1 moves to the next number.
6.
The loop stops when count becomes 6.
🔄 Three Important Parts of a while Loop
count = 1
→ Initialization
while count <= 5: → Condition
count = count + 1 → Update
while count <= 5: → Condition
count = count + 1 → Update
🔎 Step-by-Step Calculation
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
⚠️ Important:
A while loop requires the loop-control variable to be
updated. Here, count = count + 1 ensures that
count eventually becomes 6 and the loop terminates.
➕ 3. Sum of Integers from 1 to 100
➜ This Python program uses a while loop to calculate the sum of all integers from 1 to 100.
▶ Sample Output
Sum of integers from 1 to 100 is: 5050
💡 How It Works
1.
sum is initialized to 0.
2.
i starts at 1.
3.
The loop runs while i <= 100.
4.
Each value of i is added to sum.
5.
i = i + 1 moves to the next integer.
6.
When i becomes 101, the condition becomes false
and the loop stops.
🔄 From for Loop to while Loop
The original for loop can be represented using
three important parts in a while loop:
i = 1 → Initialization
while i <= 100: → Condition
i = i + 1 → Update
while i <= 100: → Condition
i = i + 1 → Update
🔎 What Happens in the Loop?
1 + 2 + 3 + 4 + 5 + … + 100
= 5050
⚠️ Important:
In a while loop, the programmer must explicitly
update the control variable. Here,
i = i + 1 ensures that the loop eventually terminates.
➕ 4. Sum of First N Natural Numbers
➜ This Python program uses a while loop to calculate the sum of the first N natural numbers.
▶ Sample Output
Enter value of n: 10
Sum of n natural numbers is: 55
💡 How It Works
1.
The user enters the value of N.
2.
sum is initialized to 0 and
i starts at 1.
3.
The loop continues while i <= n.
4.
Each value of i is added to sum.
5.
i = i + 1 moves the counter to the next number.
6.
The loop stops when i becomes greater than
N.
🔄 From for Loop to while Loop
The original for loop can be expressed using
three explicit parts in a while loop:
i = 1 → Initialization
while i <= n: → Condition
i = i + 1 → Update
while i <= n: → Condition
i = i + 1 → Update
🔎 For N = 10
1 + 2 + 3 + 4 + 5 + … + 10
= 55
📌 Quick Note:
The value of N determines how many natural numbers
are added. For example, if N = 10, the program adds
the numbers from 1 to 10.
➕ 5. Sum of Even Numbers Using a while Loop
➜ This Python program uses a while loop to calculate the sum of all even numbers up to a given value of N.
▶ Sample Output
Enter value of n: 10
Sum of even numbers up to n is: 30
💡 How It Works
1.
The user enters the value of N.
2.
sum starts at 0 and
i starts at 0.
3.
The while loop continues while
i <= n.
4.
The current even number is added to sum.
5.
i = i + 2 moves directly to the next even number.
6.
The loop stops when i becomes greater than
N.
🔄 From for Loop to while Loop
In the original for loop, the step value
2 automatically moves to the next even number.
for i in range(0, n + 1, 2):
With a while loop, we perform that update ourselves:
i = i + 2
🔎 For N = 10
i takes the values:
0, 2, 4, 6, 8, 10
Therefore:
0 + 2 + 4 + 6 + 8 + 10 = 30
📌 Quick Note:
The statement i = i + 2 is important because it
skips the odd numbers and moves from one even number directly to
the next. Without this update, the loop could become infinite.
◼ 6. Sum of Squares of First N Natural Numbers
➜ This Python program uses a while loop to calculate the sum of the squares of the first N natural numbers.
▶ Sample Output
Enter value of n: 5
Sum of squares of integers up to n is: 55
💡 How It Works
1.
The user enters the value of N.
2.
sum is initialized to 0 and
i starts at 1.
3.
The loop continues while i <= n.
4.
i * i calculates the square of the current number.
5.
The square is added to sum.
6.
i = i + 1 moves the loop to the next natural number.
🔄 From for Loop to while Loop
In the original for loop, Python automatically
moves i through the required values:
for i in range(1, n + 1):
With a while loop, the initialization,
condition, and update are written explicitly:
i = 1 → Initialization
while i <= n: → Condition
i = i + 1 → Update
while i <= n: → Condition
i = i + 1 → Update
🔎 For N = 5
1² + 2² + 3² + 4² + 5²
= 1 + 4 + 9 + 16 + 25
= 55
📌 Quick Note:
The statement i = i + 1 is essential in this
while loop. It moves i to the next
natural number and ensures that the loop eventually terminates.
