Recognised as Number

13,677

Positive
Odd
Composite
5 digits

13,677 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 6.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value13,677

Digit count5

Digit sum24

Digit product882

Multiplicative persistence4times 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 factorisation3 × 47 × 97

Distinct prime factors33, 47, 97

Number of divisors8

Sum of divisors σ(n)18,816

Aliquot sum5,139sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)8,832integers below n that share no factor with it

Carmichael function λ(n)2,208the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 8,832

Möbius function μ(n)−13 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 47, 97, 141, 291, 4,559, 13,6778 in total

Arithmetic

Previous number13,676

Next number13,678

Double27,354

Half6,838.5

Square187,060,329

Cube2,558,424,119,733

Square root116.948706705≈irrational, shown to 9 decimal places

Cube root23.914627228≈

Negation-13,677

Reciprocal0.0000731154≈

Representations

Decimal13,677

Binary1101010110110114 bits

Octal32555

Hexadecimal356D

Base 36AJX

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

In wordsthirteen thousand, six hundred and seventy-seven

Ordinalthirteen thousand, six hundred and seventy-seventh

Scientific notation1.3677 × 10^4

Engineering notation13.677 × 10^3

In other bases

Ternary200202120base 3; the most digit-efficient integer base after e: 9 digits

Quinary414202base 5; one hand: 6 digits

Septenary54606base 7: 5 digits

Nonary20676base 9; each digit is two ternary digits: 5 digits

Duodecimal7ab9base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1e3hbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:47:57base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T01T10TT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100101010111101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010101101101

Bit length14 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits5within that length

Bit parityodd9 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 6d

Gray code10111111011011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010101101101

32-bit00000000000000000011010101101101

64-bit0000000000000000000000000000000000000000000000000011010101101101

One's complement1100101010010010at 16 bits, every bit flipped

Bits reversed1011011010101100at 16 bits

Rotated left by 10110101011011010at 16 bits, wrapping

Shifted left by 1110101011011010= 27,354, no wrap

Shifted right by 11101010110110= 6,838, discarding the low bit

These bits as a double6.75733584 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,679+2

Previous prime13,669−8

Distance to nearest prime2

Nearest square below13,456

Nearest square above13,689

Powers & multiples

13,677 to the power 2187,060,329

13,677 to the power 32,558,424,119,733

13,677 to the power 434,991,566,685,588,241

13,677 to the power 5478,579,657,558,790,372,157

First ten multiples13,677, 27,354, 41,031, 54,708, 68,385, 82,062, 95,739, 109,416, 123,093, 136,770

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 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 3

Divisible by 7No, remainder 6

Divisible by 8No, remainder 5

Divisible by 9No, remainder 6

Divisible by 10No, remainder 7

Divisible by 11No, remainder 4

Divisible by 12No, remainder 9

Divisible by 100No, remainder 77

Collatz (3n + 1) trajectory

Steps to reach 1151the total stopping time

Highest value reached41,0323× the starting value

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

First steps13,677 → 41,032 → 20,516 → 10,258 → 5,129 → 15,388 → 7,694 → 3,847 → 11,542 → 5,771 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,367,700%

13,677% as a decimal136.77

13,677% of 10013,677

13,677% of 1,000136,770

As a fraction of 10013,677/100

Read another way

As seconds3 hours, 47 minutes and 57 seconds

As bytes13.356 KiB

As a 24-bit colour#00356D

Keep nerding

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