363 (number)

Short description: Natural number

| <- 362 | 363 | 364 ->

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List of numbers — Integers

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Cardinal| three hundred sixty-three
Ordinal| 363rd
(three hundred sixty-third)
Factorization| 3 × 112
Divisors| 1, 3, 11, 33, 121, 363
Greek numeral| ΤΞΓ´
Roman numeral| CCCLXIII
Binary| 1011010112
Ternary| 1111103
Quaternary| 112234
Quinary| 24235
Senary| 14036
Octal| 5538
Duodecimal| 26312
Hexadecimal| 16B16
Vigesimal| I320
Base 36| A336

363 (three hundred [and] sixty-three) is the natural number following 362 and preceding 364.

## In mathematics

* It is an odd, composite, positive, real integer, composed of a prime (3) and a prime squared (112).
* 363 is a deficient number and a perfect totient number.
* 363 is a palindromic number in bases 3, 10, 11 and 32.
* 363 is a repdigit (BB) in base 32.
* The Mertens function returns 0.[1]
* Any subset of its digits is divisible by three.
* 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
* 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243).
* 363 can be expressed as the sum of three squares in four different ways: 112 \+ 112 \+ 112, 52 \+ 72 \+ 172, 12 \+ 12 \+ 192, and 132 \+ 132 \+ 52.
* 363 cubits is the solution given to Rhind Mathematical Papyrus question 50 – find the side length of an octagon with the same area as a circle 9 khet in diameter [1].

## References

1. ↑ "Sloane's A028442 : Numbers n such that Mertens' function is zero". OEIS Foundation. https://oeis.org/A028442.

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