Recognised as Number

31,337

Positive
Odd
Prime
5 digits

31,337 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 8.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value31,337

Digit count5

Digit sum17

Digit product189

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation31,337

Distinct prime factors131,337

Number of divisors2

Sum of divisors σ(n)31,338

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)31,336integers below n that share no factor with it

Carmichael function λ(n)31,336the 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, 31,3372 in total

Arithmetic

Previous number31,336

Next number31,338

Double62,674

Half15,668.5

Square982,007,569

Cube30,773,171,189,753

Square root177.022597428≈irrational, shown to 9 decimal places

Cube root31.527229332≈

Negation-31,337

Reciprocal0.0000319112≈

Representations

Decimal31,337

Binary11110100110100115 bits

Octal75151

Hexadecimal7A69

Base 36O6H

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

In wordsthirty-one thousand, three hundred and thirty-seven

Ordinalthirty-one thousand, three hundred and thirty-seventh

Scientific notation3.1337 × 10^4

Engineering notation31.337 × 10^3

In other bases

Ternary1120222122base 3; the most digit-efficient integer base after e: 10 digits

Quinary2000322base 5; one hand: 7 digits

Septenary160235base 7: 6 digits

Nonary46878base 9; each digit is two ternary digits: 5 digits

Duodecimal16175base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal3i6hbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal8:42:17base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TTT1000T0Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000111110111001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0111101001101001

Bit length15 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits6within that length

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

Highest set bitbit 14worth 16,384

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes27a 69

Gray code100011101011101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0111101001101001

32-bit00000000000000000111101001101001

64-bit0000000000000000000000000000000000000000000000000111101001101001

One's complement1000010110010110at 16 bits, every bit flipped

Bits reversed1001011001011110at 16 bits

Rotated left by 11111010011010010at 16 bits, wrapping

Shifted left by 11111010011010010= 62,674, no wrap

Shifted right by 111110100110100= 15,668, discarding the low bit

These bits as a double1.54825351 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime31,357+20

Previous prime31,333−4

Distance to nearest prime0, it is prime

Nearest square below31,329

Nearest square above31,684

Powers & multiples

31,337 to the power 2982,007,569

31,337 to the power 330,773,171,189,753

31,337 to the power 4964,338,865,573,289,761

31,337 to the power 530,219,487,030,470,181,240,457

First ten multiples31,337, 62,674, 94,011, 125,348, 156,685, 188,022, 219,359, 250,696, 282,033, 313,370

Powers of twoBetween 2^14 (16,384) and 2^15 (32,768)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 5

Divisible by 7No, remainder 5

Divisible by 8No, remainder 1

Divisible by 9No, remainder 8

Divisible by 10No, remainder 7

Divisible by 11No, remainder 9

Divisible by 12No, remainder 5

Divisible by 100No, remainder 37

Collatz (3n + 1) trajectory

Steps to reach 159the total stopping time

Highest value reached237,9767× the starting value

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

First steps31,337 → 94,012 → 47,006 → 23,503 → 70,510 → 35,255 → 105,766 → 52,883 → 158,650 → 79,325 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,133,700%

31,337% as a decimal313.37

31,337% of 10031,337

31,337% of 1,000313,370

As a fraction of 10031,337/100

Read another way

As seconds8 hours, 42 minutes and 17 seconds

As bytes30.603 KiB

As a 24-bit colour#007A69

Keep nerding

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