Recognised as Number

33,773

Positive
Odd
Prime
5 digits

33,773 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 5.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value33,773

Digit count5

Digit sum23

Digit product1,323

Multiplicative persistence3times the digit product can be taken before one digit is left

Digital root5repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation33,773

Distinct prime factors133,773

Number of divisors2

Sum of divisors σ(n)33,774

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)33,772integers below n that share no factor with it

Carmichael function λ(n)33,772the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)−11 distinct prime factor, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 33,7732 in total

Arithmetic

Previous number33,772

Next number33,774

Double67,546

Half16,886.5

Square1,140,615,529

Cube38,522,008,260,917

Square root183.774318119≈irrational, shown to 9 decimal places

Cube root32.32385972≈

Negation-33,773

Reciprocal0.0000296095≈

Representations

Decimal33,773

Binary100000111110110116 bits

Octal101755

Hexadecimal83ED

Base 36Q25

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordsthirty-three thousand, seven hundred and seventy-three

Ordinalthirty-three thousand, seven hundred and seventy-third

Scientific notation3.3773 × 10^4

Engineering notation33.773 × 10^3

In other bases

Ternary1201022212base 3; the most digit-efficient integer base after e: 10 digits

Quinary2040043base 5; one hand: 7 digits

Septenary200315base 7: 6 digits

Nonary51285base 9; each digit is two ternary digits: 5 digits

Duodecimal17665base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal448dbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:22:53base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT011000TTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000010000111101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000001111101101

Bit length16 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits7within that length

Bit parityodd9 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes283 ed

Gray code1100001000011011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000001111101101

32-bit00000000000000001000001111101101

64-bit0000000000000000000000000000000000000000000000001000001111101101

One's complement0111110000010010at 16 bits, every bit flipped

Bits reversed1011011111000001at 16 bits

Rotated left by 10000011111011011at 16 bits, wrapping

Shifted left by 110000011111011010= 67,546, no wrap

Shifted right by 1100000111110110= 16,886, discarding the low bit

These bits as a double1.66860791 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime33,791+18

Previous prime33,769−4

Distance to nearest prime0, it is prime

Nearest square below33,489

Nearest square above33,856

Powers & multiples

33,773 to the power 21,140,615,529

33,773 to the power 338,522,008,260,917

33,773 to the power 41,301,003,784,995,949,841

33,773 to the power 543,938,800,830,668,213,980,093

First ten multiples33,773, 67,546, 101,319, 135,092, 168,865, 202,638, 236,411, 270,184, 303,957, 337,730

Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 5

Divisible by 7No, remainder 5

Divisible by 8No, remainder 5

Divisible by 9No, remainder 5

Divisible by 10No, remainder 3

Divisible by 11No, remainder 3

Divisible by 12No, remainder 5

Divisible by 100No, remainder 73

Collatz (3n + 1) trajectory

Steps to reach 1111the total stopping time

Highest value reached410,88412× the starting value

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps33,773 → 101,320 → 50,660 → 25,330 → 12,665 → 37,996 → 18,998 → 9,499 → 28,498 → 14,249 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,377,300%

33,773% as a decimal337.73

33,773% of 10033,773

33,773% of 1,000337,730

As a fraction of 10033,773/100

Read another way

As seconds9 hours, 22 minutes and 53 seconds

As bytes32.981 KiB

As a 24-bit colour#0083ED

Keep nerding

Every link below is a page Nerdulator can generate from what it already knows about this value.