240

Number
$240$ (two hundred and forty) is:


 * $2^4 \times 3 \times 5$


 * The length of the longest edge of the smallest cuboid whose edges and the diagonals of whose faces are all integers:
 * The lengths of the edges are $44, 117, 240$
 * The lengths of the diagonals of the faces are $125, 244, 267$.


 * The $9$th positive integer after $64$, $96$, $128$, $144$, $160$, $192$, $216$, $224$ with $6$ or more prime factors:
 * $240 = 2 \times 2 \times 2 \times 2 \times 3 \times 5$


 * The $12$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$:
 * $\map \tau {240} = 20$


 * The $12$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$:
 * $\dfrac {\map \sigma {240} } {240} = \dfrac {744} {240} = 3 \cdotp 1$


 * The $29$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$, $20$, $24$, $30$, $36$, $42$, $48$, $60$, $72$, $84$, $90$, $96$, $108$, $120$, $144$, $168$, $180$, $210$, $216$:
 * $\map \sigma {240} = 744$


 * An integer with over $240$ divisors is greater than $1 \, 000 \, 000$.

Also see

 * Tau Function of 240


 * Cuboid with Integer Edges and Face Diagonals
 * Number with over 240 Divisors is greater than 1,000,000