120

Number
$120$ (one hundred and twenty) is:


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


 * The $10$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$:
 * $\tau \left({120}\right) = 16$


 * The $23$rd highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, 72, 84, 90, 96, 108$:
 * $\sigma \left({120}\right) = 360$


 * The $10$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$:
 * $\dfrac {\sigma \left({120}\right)} {120} = \dfrac {360} {120} = 3$


 * The $15$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$:
 * $120 = \displaystyle \sum_{k \mathop = 1}^{15} k = \dfrac {15 \times \left({15 + 1}\right)} 2$


 * The $8$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$:
 * $120 = 1 + 5 + 9 + 13 + 17 + 21 + 25 + 29 = 8 \left({2 \times 8 - 1}\right)$


 * The $8$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$, $56$, $84$:
 * $120 = 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 = \dfrac {8 \left({8 + 1}\right) \left({8 + 2}\right)} 6$


 * The $3$rd after $1$, $10$ of the $5$ tetrahedral numbers which are also triangular.


 * The smallest positive integer greater than $1$ to appear $6$ times in Pascal's Triangle.


 * The $5$th factorial after $1$, $2$, $6$, $24$:
 * $120 = 5! = 5 \times 4 \times 3 \times 2 \times 1$


 * The $6$th untouchable number after $2$, $5$, $52$, $88$, $96$.


 * There are $17$ positive integers which have an Euler $\phi$ value $120$.


 * The smallest positive integer which can be expressed as the sum of $2$ odd primes in $12$ ways.


 * The $1$st triperfect number:
 * $\sigma \left({120}\right) = 360 = 3 \times 120$


 * The $4$th and final element of the Fermat set after $1$, $3$, $8$


 * The $2$nd after $24$ of the $3$ integers which can be expressed as the product of both $3$ and $4$ consecutive integers:
 * $120 = 4 \times 5 \times 6 = 2 \times 3 \times 4 \times 5$


 * The $2$nd triangular number which can be expressed as the product of $3$ consecutive integers:
 * $120 = T_{15} = 4 \times 5 \times 6$

Also see

 * Numbers with Euler Phi Value of 120