Recognised as Number

31,801

Positive
Odd
Composite
5 digits

31,801 is an odd 5-digit integer and a composite number. It has 12 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value31,801

Digit count5

Digit sum13

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times the digit product can be taken before one digit is left

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation7^2 × 11 × 59

Distinct prime factors37, 11, 59

Number of divisors12

Sum of divisors σ(n)41,040

Aliquot sum9,239sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)24,360integers below n that share no factor with it

Carmichael function λ(n)6,090the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 24,360

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 7, 11, 49, 59, 77, 413, 539, 649, 2,891, 4,543, 31,80112 in total

Arithmetic

Previous number31,800

Next number31,802

Double63,602

Half15,900.5

Square1,011,303,601

Cube32,160,465,815,401

Square root178.32834884≈irrational, shown to 9 decimal places

Cube root31.682073143≈

Negation-31,801

Reciprocal0.0000314456≈

Representations

Decimal31,801

Binary11111000011100115 bits

Octal76071

Hexadecimal7C39

Base 36OJD

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

In wordsthirty-one thousand, eight hundred and one

Ordinalthirty-one thousand, eight hundred and first

Scientific notation3.1801 × 10^4

Engineering notation31.801 × 10^3

In other bases

Ternary1121121211base 3; the most digit-efficient integer base after e: 10 digits

Quinary2004201base 5; one hand: 7 digits

Septenary161500base 7: 6 digits

Nonary47554base 9; each digit is two ternary digits: 5 digits

Duodecimal164a1base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal3ja1base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal8:50:1base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT0TT0TT11digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000110001001001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0111110000111001

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

Bytes27c 39

Gray code100001000100101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0111110000111001

32-bit00000000000000000111110000111001

64-bit0000000000000000000000000000000000000000000000000111110000111001

One's complement1000001111000110at 16 bits, every bit flipped

Bits reversed1001110000111110at 16 bits

Rotated left by 11111100001110010at 16 bits, wrapping

Shifted left by 11111100001110010= 63,602, no wrap

Shifted right by 111111000011100= 15,900, discarding the low bit

These bits as a double1.57117816 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime31,817+16

Previous prime31,799−2

Distance to nearest prime2

Nearest square below31,684

Nearest square above32,041

Powers & multiples

31,801 to the power 21,011,303,601

31,801 to the power 332,160,465,815,401

31,801 to the power 41,022,734,973,395,567,201

31,801 to the power 532,523,994,888,952,432,559,001

First ten multiples31,801, 63,602, 95,403, 127,204, 159,005, 190,806, 222,607, 254,408, 286,209, 318,010

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 1

Divisible by 6No, remainder 1

Divisible by 7Yes

Divisible by 8No, remainder 1

Divisible by 9No, remainder 4

Divisible by 10No, remainder 1

Divisible by 11Yes

Divisible by 12No, remainder 1

Divisible by 100No, remainder 1

Collatz (3n + 1) trajectory

Steps to reach 1129the total stopping time

Highest value reached107,3323× the starting value

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

First steps31,801 → 95,404 → 47,702 → 23,851 → 71,554 → 35,777 → 107,332 → 53,666 → 26,833 → 80,500 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,180,100%

31,801% as a decimal318.01

31,801% of 10031,801

31,801% of 1,000318,010

As a fraction of 10031,801/100

Read another way

As seconds8 hours, 50 minutes and 1 second

As bytes31.056 KiB

As a 24-bit colour#007C39

Keep nerding

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