How do you find all factors of a number in Python?

Loop i from 1 to n (use range(1, n+1), not starting at 0). If n % i == 0, then i is a factor—print or collect it. Modulo % gives remainder; remainder 0 means i divides n exactly.

Why not start the factor loop at 0 in Python?

Dividing by zero is undefined. n % 0 would raise ZeroDivisionError. Always start at 1 when checking factors with modulo.

How do you check if a number is prime in Python?

A prime has exactly two positive factors: 1 and itself. Count factors with a loop; if count == 2, the number is prime. Note: 1 is not prime because it has only one factor.

What does n % i == 0 mean?

It means n divided by i has remainder zero—i divides n evenly. That is the standard test for whether i is a factor of n.

Practice Problem - Factors of a Number & Prime Check - Beginner's Guide - Vimal Thapliyal

Factors of a number: all integers from 1 to n that divide n exactly (remainder 0). Check with n % i == 0. Loop i from 1 to n (NOT 0 – avoid division by zero!).
Prime number: a number with exactly TWO factors (1 and itself). So count the factors; if count == 2, it's prime; otherwise not.

Let’s go! 🚀

Part 1: What Are Factors?

📌 A factor of a number n is any integer that divides n exactly (remainder 0).

Example: Factors of 12

12 ÷ 1 = 12 remainder 0 → 1 is a factor
12 ÷ 2 = 6 remainder 0 → 2 is a factor
12 ÷ 3 = 4 remainder 0 → 3 is a factor
12 ÷ 4 = 3 remainder 0 → 4 is a factor
12 ÷ 5 = 2 remainder 2 → 5 is NOT a factor
12 ÷ 6 = 2 remainder 0 → 6 is a factor
7, 8, 9, 10, 11 don't divide 12 exactly
12 ÷ 12 = 1 remainder 0 → 12 is a factor

So factors of 12 are: 1, 2, 3, 4, 6, 12.

How to check in code: n % i == 0 means "i divides n exactly."

Demo: Factors of 12

n = 12
for i in range(1, n + 1):
    if n % i == 0:
        print(f"   {i} is a factor (12 % {i} = 0)")

Part 2: Loop from 1 to n (NOT 0!)

📌 We must check i = 1, 2, 3, ..., n. So: for i in range(1, n+1):

⚠️ Do NOT use range(0, n+1). If i is 0, then n % 0 causes "division by zero" error! Always start from 1: range(1, n+1).

Part 3: Program – Print All Factors

Steps:

n = int(input("Enter a number: "))
for i in range(1, n + 1):
    if n % i == 0:
        print(i)

Demo: Factors of 12 (one line)

n = 12
factors = [i for i in range(1, n + 1) if n % i == 0]
print("   ", factors)

Part 4: What is a Prime Number?

📌 A prime number has exactly TWO factors: 1 and the number itself.

Examples:

11 → Factors: 1 and 11 only. So 11 is prime.
10 → Factors: 1, 2, 5, 10 (four factors). So 10 is not prime.
7 → Factors: 1 and 7 only. So 7 is prime.

So the rule: count the factors. If count == 2 → prime; otherwise not prime.

Part 5: Program – Prime Check

Steps:

n = int(input("Enter a number: "))
count = 0
for i in range(1, n + 1):
    if n % i == 0:
        count += 1
if count == 2:
    print("Prime")
else:
    print("Not prime")

Same loop as factors; we just count instead of printing. If count is 2, it's prime.

Demo: Prime check for 11 and 10

for n in [11, 10]:
    count = 0
    for i in range(1, n + 1):
        if n % i == 0:
            count += 1
    print(f"   {n}: {count} factors → {'Prime' if count == 2 else 'Not prime'}")

Part 6: Summary

✅ Factors: for i in range(1, n+1): if n % i == 0: print(i) (Always start from 1 to avoid division by zero.)

✅ Prime: Count factors. If count == 2 → prime; else → not prime. count = 0; for i in range(1, n+1): if n % i == 0: count += 1 if count == 2: print("Prime") else: print("Not prime")

Congratulations! You now understand Factors and Prime Number Check in Python! 🎉

Key Takeaways:

Use n % i == 0 to test if i is a factor
Loop from 1 to n (never 0)
Prime = exactly 2 factors (1 and itself)
Count factors or stop early when count > 2

Next Steps:

Practice with user input
Try printing only prime factors
Optimize: loop only to sqrt(n) for faster prime check