ITPEC FE Subject B April 2025 Question 2

Perfect number check — fill in the condition and accumulator for summing divisors.

A perfect number equals the sum of its proper divisors (all positive divisors excluding itself). The program loops k from 1 to n ÷ 2 and needs to:
- A (condition): check if k divides n → n mod k = 0
- B (accumulate): add the divisor itself → sum ← sum + k

Trace with n = 28:
- k=1: 28 mod 1 = 0 → sum = 0+1 = 1
- k=2: 28 mod 2 = 0 → sum = 1+2 = 3
- k=3: 28 mod 3 ≠ 0 → skip
- k=4: 28 mod 4 = 0 → sum = 3+4 = 7
- k=7: 28 mod 7 = 0 → sum = 7+7 = 14
- k=14: 28 mod 14 = 0 → sum = 14+14 = 28
- sum = 28 = n → return true ✓

Why not others:
- (a) n mod k ≠ 0 selects non-divisors; sum + 1 counts instead of summing
- (b) n mod k ≠ 0 selects non-divisors (wrong filter)
- (c) n mod k = 0 is correct, but sum + 1 counts divisors instead of summing them

Key rule: to sum divisors, check n mod k = 0 (divisibility) and accumulate k itself, not 1.

AI-generated — may contain errors