Recognised as Number

13,477

Positive
Odd
Prime
5 digits

13,477 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value13,477

Digit count5

Digit sum22

Digit product588

Multiplicative persistence3times 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 factorisation13,477

Distinct prime factors113,477

Number of divisors2

Sum of divisors σ(n)13,478

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)13,476integers below n that share no factor with it

Carmichael function λ(n)13,476the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)−11 distinct prime factor, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 13,4772 in total

Arithmetic

Previous number13,476

Next number13,478

Double26,954

Half6,738.5

Square181,629,529

Cube2,447,821,162,333

Square root116.090481953≈irrational, shown to 9 decimal places

Cube root23.797485788≈

Negation-13,477

Reciprocal0.0000742005≈

Representations

Decimal13,477

Binary1101001010010114 bits

Octal32245

Hexadecimal34A5

Base 36AED

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

In wordsthirteen thousand, four hundred and seventy-seven

Ordinalthirteen thousand, four hundred and seventy-seventh

Scientific notation1.3477 × 10^4

Engineering notation13.477 × 10^3

In other bases

Ternary200111011base 3; the most digit-efficient integer base after e: 9 digits

Quinary412402base 5; one hand: 6 digits

Septenary54202base 7: 5 digits

Nonary20434base 9; each digit is two ternary digits: 5 digits

Duodecimal7971base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1ddhbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:44:37base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T00111011digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary111010111100101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010010100101

Bit length14 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits7within that length

Bit parityodd7 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

Bytes234 a5

Gray code10111011110111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010010100101

32-bit00000000000000000011010010100101

64-bit0000000000000000000000000000000000000000000000000011010010100101

One's complement1100101101011010at 16 bits, every bit flipped

Bits reversed1010010100101100at 16 bits

Rotated left by 10110100101001010at 16 bits, wrapping

Shifted left by 1110100101001010= 26,954, no wrap

Shifted right by 11101001010010= 6,738, discarding the low bit

These bits as a double6.65852271 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,487+10

Previous prime13,469−8

Distance to nearest prime0, it is prime

Nearest square below13,456

Nearest square above13,689

Powers & multiples

13,477 to the power 2181,629,529

13,477 to the power 32,447,821,162,333

13,477 to the power 432,989,285,804,761,841

13,477 to the power 5444,596,604,790,775,331,157

First ten multiples13,477, 26,954, 40,431, 53,908, 67,385, 80,862, 94,339, 107,816, 121,293, 134,770

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 1

Divisible by 7No, remainder 2

Divisible by 8No, remainder 5

Divisible by 9No, remainder 4

Divisible by 10No, remainder 7

Divisible by 11No, remainder 2

Divisible by 12No, remainder 1

Divisible by 100No, remainder 77

Collatz (3n + 1) trajectory

Steps to reach 1182the total stopping time

Highest value reached138,40010× the starting value

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

First steps13,477 → 40,432 → 20,216 → 10,108 → 5,054 → 2,527 → 7,582 → 3,791 → 11,374 → 5,687 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,347,700%

13,477% as a decimal134.77

13,477% of 10013,477

13,477% of 1,000134,770

As a fraction of 10013,477/100

Read another way

As seconds3 hours, 44 minutes and 37 seconds

As bytes13.161 KiB

As a 24-bit colour#0034A5

Keep nerding

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