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# 162 (number)

 ← 161 162 163 →
Cardinalone hundred sixty-two
Ordinal162nd
(one hundred sixty-second)
Factorization2 × 34
Divisors1, 2, 3, 6, 9, 18, 27, 54, 81, 162
Greek numeralΡΞΒ´
Roman numeralCLXII
Binary101000102
Ternary200003
Quaternary22024
Quinary11225
Senary4306
Octal2428
Duodecimal11612
Vigesimal8220
Base 364I36

162 (one hundred [and] sixty-two) is the natural number between 161 and 163.

## In mathematics

Having only 2 and 3 as its prime divisors, 162 is a 3-smooth number.[1] 162 is also an abundant number, since its sum of divisors ${\displaystyle 1+2+3+6+9+18+27+54+81=201}$ is greater than it.[2] As the product ${\displaystyle 3\times 6\times 9=162}$ of numbers three units apart from each other, it is a triple factorial number.[3]

There are 162 ways of partitioning seven items into subsets of at least two items per subset.[4]

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A003586 (3-smooth numbers: numbers of the form 2^i*3^j with i, j >= 0)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation..
2. ^ Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
3. ^ Sloane, N. J. A. (ed.). "Sequence A007661 (Triple factorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
4. ^ Sloane, N. J. A. (ed.). "Sequence A000296 (Set partitions without singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
5. ^ Karpin, Howie (2011), 162-0: Imagine a Mets Perfect Season, Triumph Books, ISBN 9781623684440.
6. ^ Formosa, Dan; Hamburger, Paul (2009), Baseball Field Guide: An In-Depth Illustrated Guide to the Complete Rules of Baseball, Da Capo Press, p. 23, ISBN 9780786732098.