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# 363 (number)

 ← 362 363 364 →
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
Vigesimal I320
Base 36 A336

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

## In mathematics

• 363 is the sum of nine consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59).
• It is an odd, composite, positive, real integer, composed of a prime (3) and a prime squared (112).
• The 363rd day in a year is 29 December (28 December in leap years).
• 363 is a palindromic number in bases 3, 10, 11 and 32.
• Any subset of its digits is divisible by three.
• 363 is a repdigit (BB) in base 32.
• 363 is a 122-gonal number.
• 363 is a deficient number.
• 363 is the sum of five consecutive powers of 3 (3 + 9 + 27 + 81 + 243) deficient number.
• The Mertens function returns 0.[1]
• 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].
• 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 is a perfect totient number.

## References

1. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-02.