840

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Number

$840$ (eight hundred and forty) is:

$2^3 \times 3 \times 5 \times 7$

The $15$th highly composite number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$:

$\map {\sigma_0} {840} = 32$

The $15$th superabundant number after $1$, $2$, $4$, $6$, $12$, $24$, $36$, $48$, $60$, $120$, $180$, $240$, $360$, $720$:

$\dfrac {\map {\sigma_1} {840} } {840} = \dfrac {2880} {840} \approx 3 \cdotp 429$

The $42$nd highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $210$, $216$, $240$, $288$, $300$, $336$, $360$, $420$, $480$, $504$, $600$, $630$, $660$, $720$:

$\map {\sigma_1} {840} = 2880$

Has the largest divisor count of all the positive integers up to $1000$:

$\map {\sigma_0} {840} = 32$

Arithmetic Functions on $840$

\(\ds \map {\sigma_0} { 840 }\)

\(=\)

\(\ds 32\)

$\sigma_0$ of $840$

\(\ds \map {\sigma_1} { 840 }\)

\(=\)

\(\ds 2880\)

$\sigma_1$ of $840$

Also see

• Previous  ... Next: Highly Abundant Number
• Previous  ... Next: Highly Composite Number
• Previous  ... Next: Superabundant Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $840$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $840$