Recognised as Number

13,791

Positive
Odd
Composite
5 digits

13,791 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 3.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value13,791

Digit count5

Digit sum21

Digit product189

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

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation3 × 4,597

Distinct prime factors23, 4,597

Number of divisors4

Sum of divisors σ(n)18,392

Aliquot sum4,601sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)9,192integers below n that share no factor with it

Carmichael function λ(n)4,596the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 9,192

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 4,597, 13,7914 in total

Arithmetic

Previous number13,790

Next number13,792

Double27,582

Half6,895.5

Square190,191,681

Cube2,622,933,472,671

Square root117.435088453≈irrational, shown to 9 decimal places

Cube root23.980887562≈

Negation-13,791

Reciprocal0.0000725111≈

Representations

Decimal13,791

Binary1101011101111114 bits

Octal32737

Hexadecimal35DF

Base 36AN3

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

In wordsthirteen thousand, seven hundred and ninety-one

Ordinalthirteen thousand, seven hundred and ninety-first

Scientific notation1.3791 × 10^4

Engineering notation13.791 × 10^3

In other bases

Ternary200220210base 3; the most digit-efficient integer base after e: 9 digits

Quinary420131base 5; one hand: 6 digits

Septenary55131base 7: 5 digits

Nonary20823base 9; each digit is two ternary digits: 5 digits

Duodecimal7b93base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1e9bbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:49:51base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T010T1T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100101000100011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010111011111

Bit length14 bitsto write the magnitude

Set bits11the population count, or Hamming weight

Zero bits3within that length

Bit parityodd11 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 13worth 8,192

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes235 df

Gray code10111100110000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010111011111

32-bit00000000000000000011010111011111

64-bit0000000000000000000000000000000000000000000000000011010111011111

One's complement1100101000100000at 16 bits, every bit flipped

Bits reversed1111101110101100at 16 bits

Rotated left by 10110101110111110at 16 bits, wrapping

Shifted left by 1110101110111110= 27,582, no wrap

Shifted right by 11101011101111= 6,895, discarding the low bit

These bits as a double6.81365932 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,799+8

Previous prime13,789−2

Distance to nearest prime2

Nearest square below13,689

Nearest square above13,924

Powers & multiples

13,791 to the power 2190,191,681

13,791 to the power 32,622,933,472,671

13,791 to the power 436,172,875,521,605,761

13,791 to the power 5498,860,126,318,465,049,951

First ten multiples13,791, 27,582, 41,373, 55,164, 68,955, 82,746, 96,537, 110,328, 124,119, 137,910

Powers of twoBetween 2^13 (8,192) and 2^14 (16,384)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 3

Divisible by 5No, remainder 1

Divisible by 6No, remainder 3

Divisible by 7No, remainder 1

Divisible by 8No, remainder 7

Divisible by 9No, remainder 3

Divisible by 10No, remainder 1

Divisible by 11No, remainder 8

Divisible by 12No, remainder 3

Divisible by 100No, remainder 91

Collatz (3n + 1) trajectory

Steps to reach 189the total stopping time

Highest value reached209,46415× the starting value

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

First steps13,791 → 41,374 → 20,687 → 62,062 → 31,031 → 93,094 → 46,547 → 139,642 → 69,821 → 209,464 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,379,100%

13,791% as a decimal137.91

13,791% of 10013,791

13,791% of 1,000137,910

As a fraction of 10013,791/100

Read another way

As seconds3 hours, 49 minutes and 51 seconds

As bytes13.468 KiB

As a 24-bit colour#0035DF

Keep nerding

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