Recognised as Number

13,667

Positive
Odd
Composite
5 digits

13,667 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 5.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value13,667

Digit count5

Digit sum23

Digit product756

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 factorisation79 × 173

Distinct prime factors279, 173

Number of divisors4

Sum of divisors σ(n)13,920

Aliquot sum253sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)13,416integers below n that share no factor with it

Carmichael function λ(n)6,708the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 13,416

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

SquarefreeYesno repeated prime factor

All divisors1, 79, 173, 13,6674 in total

Arithmetic

Previous number13,666

Next number13,668

Double27,334

Half6,833.5

Square186,786,889

Cube2,552,816,411,963

Square root116.905945101≈irrational, shown to 9 decimal places

Cube root23.908797378≈

Negation-13,667

Reciprocal0.0000731689≈

Representations

Decimal13,667

Binary1101010110001114 bits

Octal32543

Hexadecimal3563

Base 36AJN

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

In wordsthirteen thousand, six hundred and sixty-seven

Ordinalthirteen thousand, six hundred and sixty-seventh

Scientific notation1.3667 × 10^4

Engineering notation13.667 × 10^3

In other bases

Ternary200202012base 3; the most digit-efficient integer base after e: 9 digits

Quinary414132base 5; one hand: 6 digits

Septenary54563base 7: 5 digits

Nonary20665base 9; each digit is two ternary digits: 5 digits

Duodecimal7aabbase 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1e37base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:47:47base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T01T1T1TTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100101010100111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010101100011

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 odd

Highest set bitbit 13worth 8,192

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes235 63

Gray code10111111010010n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010101100011

32-bit00000000000000000011010101100011

64-bit0000000000000000000000000000000000000000000000000011010101100011

One's complement1100101010011100at 16 bits, every bit flipped

Bits reversed1100011010101100at 16 bits

Rotated left by 10110101011000110at 16 bits, wrapping

Shifted left by 1110101011000110= 27,334, no wrap

Shifted right by 11101010110001= 6,833, discarding the low bit

These bits as a double6.75239518 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,669+2

Previous prime13,649−18

Distance to nearest prime2

Nearest square below13,456

Nearest square above13,689

Powers & multiples

13,667 to the power 2186,786,889

13,667 to the power 32,552,816,411,963

13,667 to the power 434,889,341,902,298,321

13,667 to the power 5476,832,635,778,711,153,107

First ten multiples13,667, 27,334, 41,001, 54,668, 68,335, 82,002, 95,669, 109,336, 123,003, 136,670

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 3

Divisible by 5No, remainder 2

Divisible by 6No, remainder 5

Divisible by 7No, remainder 3

Divisible by 8No, remainder 3

Divisible by 9No, remainder 5

Divisible by 10No, remainder 7

Divisible by 11No, remainder 5

Divisible by 12No, remainder 11

Divisible by 100No, remainder 67

Collatz (3n + 1) trajectory

Steps to reach 158the total stopping time

Highest value reached61,5044× the starting value

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

First steps13,667 → 41,002 → 20,501 → 61,504 → 30,752 → 15,376 → 7,688 → 3,844 → 1,922 → 961 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,366,700%

13,667% as a decimal136.67

13,667% of 10013,667

13,667% of 1,000136,670

As a fraction of 10013,667/100

Read another way

As seconds3 hours, 47 minutes and 47 seconds

As bytes13.347 KiB

As a 24-bit colour#003563

Keep nerding

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