The smallest tetrahedral number that is the product of
two tetrahedral
numbers both greater than one. Also the second smallest number and smallest tetrahedral number divisible by 1, 4, 10, 20, 35, and 56 (the first
six tetrahedral numbers; the smallest number divisible by all those is 280)
tetra(3) * tetra(6) = (3*4*5/6)*(6*7*8/6) = (3*4*5/6)*(7*8) = (
60/6)*56 = 10*56 = 560 = tetra(14). 560/4=140, 560/10= 56, 560/20=
28, 560/35= 16, 560/56= 10 (all quotients are
even so 280, half of 560, is divisible by all divisors given (1, 4, 10, 20, 35, and 56)).