Recognised as Number

13,794

Positive
Even
Composite
5 digits

13,794 is an even 5-digit integer and a composite number. It has 24 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value13,794

Digit count5

Digit sum24

Digit product756

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

Digital root6repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2 × 3 × 11^2 × 19

Distinct prime factors42, 3, 11, 19

Number of divisors24

Sum of divisors σ(n)31,920

Aliquot sum18,126sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)3,960integers below n that share no factor with it

Carmichael function λ(n)990the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 3,960

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 6, 11, 19, 22, 33, 38, 57, 66, 114, 121, 209, 242, 363, 418, 627, 726, 1,254, 2,299, 4,598, 6,897, 13,79424 in total

Arithmetic

Previous number13,793

Next number13,795

Double27,588

Half6,897

Square190,274,436

Cube2,624,645,570,184

Square root117.447860772≈irrational, shown to 9 decimal places

Cube root23.982626315≈

Negation-13,794

Reciprocal0.0000724953≈

Representations

Decimal13,794

Binary1101011110001014 bits

Octal32742

Hexadecimal35E2

Base 36AN6

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

In wordsthirteen thousand, seven hundred and ninety-four

Ordinalthirteen thousand, seven hundred and ninety-fourth

Scientific notation1.3794 × 10^4

Engineering notation13.794 × 10^3

In other bases

Ternary200220220base 3; the most digit-efficient integer base after e: 9 digits

Quinary420134base 5; one hand: 6 digits

Septenary55134base 7: 5 digits

Nonary20826base 9; each digit is two ternary digits: 5 digits

Duodecimal7b96base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1e9ebase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:49:54base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T010T10T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100101000100110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010111100010

Bit length14 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits6within that length

Bit parityeven8 set bits, so even; not the same as the number itself being even

Highest set bitbit 13worth 8,192

Lowest set bitbit 11 trailing zero

Power of twoNo

Bytes235 e2

Gray code10111100010011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010111100010

32-bit00000000000000000011010111100010

64-bit0000000000000000000000000000000000000000000000000011010111100010

One's complement1100101000011101at 16 bits, every bit flipped

Bits reversed0100011110101100at 16 bits

Rotated left by 10110101111000100at 16 bits, wrapping

Shifted left by 1110101111000100= 27,588, no wrap

Shifted right by 11101011110001= 6,897, discarding the low bit

These bits as a double6.81514152 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,799+5

Previous prime13,789−5

Distance to nearest prime5

Nearest square below13,689

Nearest square above13,924

Powers & multiples

13,794 to the power 2190,274,436

13,794 to the power 32,624,645,570,184

13,794 to the power 436,204,360,995,118,096

13,794 to the power 5499,402,955,566,659,016,224

First ten multiples13,794, 27,588, 41,382, 55,176, 68,970, 82,764, 96,558, 110,352, 124,146, 137,940

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4No, remainder 2

Divisible by 5No, remainder 4

Divisible by 6Yes

Divisible by 7No, remainder 4

Divisible by 8No, remainder 2

Divisible by 9No, remainder 6

Divisible by 10No, remainder 4

Divisible by 11Yes

Divisible by 12No, remainder 6

Divisible by 100No, remainder 94

Collatz (3n + 1) trajectory

Steps to reach 1107the total stopping time

Highest value reached20,6921× the starting value

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

First steps13,794 → 6,897 → 20,692 → 10,346 → 5,173 → 15,520 → 7,760 → 3,880 → 1,940 → 970 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,379,400%

13,794% as a decimal137.94

13,794% of 10013,794

13,794% of 1,000137,940

As a fraction of 10013,794/100

Read another way

As seconds3 hours, 49 minutes and 54 seconds

As bytes13.471 KiB

As a 24-bit colour#0035E2

Keep nerding

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