# Only Number which is Sum of 3 Factors is 6

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## Contents

## Theorem

The only positive integer which is the sum of exactly $3$ of its divisors is $6$.

## Corollary

$1$ can be expressed uniquely as the sum of $3$ distinct unit fractions:

- $1 = \dfrac 1 2 + \dfrac 1 3 + \dfrac 1 6$

## Proof

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $6$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $6$