Exercise · ZW-PERFECT-NUMBER-006 · ★★☆ Intermediate
Compute the sum of the proper divisors of 12 and state whether 12 is perfect.
Choose one option.
Show answer
- C. It sums to 16, not perfect.
Explanation
The proper divisors of 12 are 1, 2, 3, 4, and 6, and they sum to 16. Since 16 does not equal 12, the number is not perfect.
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-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?
- ZW-PERFECT-NUMBER-009 Which of the following statements is false?