L3.3: While to Compute Factorial

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Learning outcomes

• define factorial mathematically
• implement factorial using while
• trace factorial loops for any n
• handle edge cases (0, negative input)

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Factorial definition

• n! = n * (n-1) * (n-2) * ... * 1
• 0! = 1

• 5! = 120
• 3! = 6

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Standard while solution

n = int(input("Enter n: "))

if n < 0:
    print("Factorial not defined for negatives")
else:
    fact = 1
    i = 1
    while i <= n:
        fact *= i
        i += 1
    print(fact)

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Why initialize fact = 1

• multiplicative identity is 1
• starting at 0 would make final answer always 0

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Dry run for n = 5

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Compact variant

n = int(input())
fact, i = 1, 1
while i <= n:
    fact *= i
    i += 1
print(fact)

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Common mistakes

• fact = 0 (wrong start)
• while i < n (misses multiplying by n)
• forgetting i += 1
• not handling negative n

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Exam hints and traps

• always remember 0! = 1
• for n = 1, output is 1
• negative inputs are invalid for standard factorial

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Practice

1. Write factorial using descending loop (i = n down to 1).
2. Predict output for n = 0.
3. Fix bug:

n = 4
fact = 1
i = 1
while i < n:
    fact *= i
    i += 1
print(fact)

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Answer key

fact = 1
i = n
while i >= 1:
    fact *= i
    i -= 1

2. 1
3. condition should be while i <= n: