2520 equals Sum of 4 Divisors in 6 Ways

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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