# 2520 equals Sum of 4 Divisors in 6 Ways

From ProofWiki

## Theorem

The number $2520$ can be expressed as the sum of $4$ of its divisors in $6$ different ways:

\(\displaystyle 2520\) | \(=\) | \(\displaystyle 1260 + 630 + 504 + 126\) | $\quad$ | $\quad$ | |||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 1260 + 630 + 421 + 210\) | $\quad$ | $\quad$ | |||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 1260 + 840 + 360 + 60\) | $\quad$ | $\quad$ | |||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 1260 + 840 + 315 + 105\) | $\quad$ | $\quad$ | |||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 1260 + 840 + 280 + 140\) | $\quad$ | $\quad$ | |||||||||

\(\displaystyle \) | \(=\) | \(\displaystyle 1260 + 840 + 252 + 168\) | $\quad$ | $\quad$ |

This is the maximum possible number of ways it is possible to express an integer as the sum of $4$ of its divisors.

## Proof

## Sources

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $2520$