560

Number

$560$ (five hundred and sixty) is:

$2^4 \times 5 \times 7$

The $14$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $96$, $133$, $176$, $225$, $280$, $341$, $408$, $481$:

$560 = \ds \sum_{k \mathop = 1}^{14} \paren {6 k - 5} = 14 \paren {3 \times 14 - 2}$

The $14$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$, $120$, $165$, $220$, $286$, $364$, $455$:

$560 = \ds \sum_{k \mathop = 1}^{14} \frac {k \paren {k + 1} } 2 = \dfrac {14 \paren {14 + 1} \paren {14 + 2} } 6$