Exercise · ZW-PERFECT-NUMBER-009 · ★★★ Advanced
Which of the following statements is false?
Choose one option.
Show answer
- D. Every number with exactly four divisors is perfect.
Explanation
The number 8 has four divisors (1, 2, 4, and 8), but its proper divisors sum to 7, so it is not perfect. The other three statements are true.
Review the concept: Perfect number
A perfect number is a positive integer \(n\) equal to the sum of its proper divisors, those smaller than \(n\); with the divisor-sum function \(\sigma\), the sum of all its divisors is twice \(n\).
\[\sigma(n)=2n\]
More practice problems: perfect number
- ZW-PERFECT-NUMBER-001 Which of these numbers is perfect?
- ZW-PERFECT-NUMBER-002 What is the second smallest perfect number?
- ZW-PERFECT-NUMBER-003 Which of these values of n satisfies the definition of a perfect number?
- ZW-PERFECT-NUMBER-004 How much do the proper divisors of 28 sum to?
- ZW-PERFECT-NUMBER-005 Which of these statements defines a perfect number n?
- ZW-PERFECT-NUMBER-006 Compute the sum of the proper divisors of 12 and state whether 12 is perfect.
- ZW-PERFECT-NUMBER-007 What is the third smallest perfect number?
- ZW-PERFECT-NUMBER-008 If 2^p-1 is prime with p=7, which perfect number does Euclid's formula give?