780

Number
$780$ (seven hundred and eighty) is:


 * $2^2 \times 3 \times 5 \times 13$


 * The $39$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $325$, $351$, $378$, $406$, $435$, $465$, $496$, $528$, $561$, $595$, $630$, $666$, $703$, $741$:
 * $780 = \displaystyle \sum_{k \mathop = 1}^{39} k = \dfrac {39 \times \left({39 + 1}\right)} 2$


 * The $20$th hexagonal number after $1, 6, 15, 28, 45, 66, 91, \ldots, 378, 435, 496, 561, 630, 703$:
 * $780 = \displaystyle \sum_{k \mathop = 1}^{20} \left({4 k - 3}\right) = 20 \left({2 \times 20 - 1}\right)$