Recognised as Number

13,471

Positive
Odd
Composite
5 digits

13,471 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 7.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value13,471

Digit count5

Digit sum16

Digit product84

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

Digital root7repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation19 × 709

Distinct prime factors219, 709

Number of divisors4

Sum of divisors σ(n)14,200

Aliquot sum729sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)12,744integers below n that share no factor with it

Carmichael function λ(n)2,124the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 12,744

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

SquarefreeYesno repeated prime factor

All divisors1, 19, 709, 13,4714 in total

Arithmetic

Previous number13,470

Next number13,472

Double26,942

Half6,735.5

Square181,467,841

Cube2,444,553,286,111

Square root116.064637164≈irrational, shown to 9 decimal places

Cube root23.793953693≈

Negation-13,471

Reciprocal0.0000742335≈

Representations

Decimal13,471

Binary1101001001111114 bits

Octal32237

Hexadecimal349F

Base 36AE7

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

In wordsthirteen thousand, four hundred and seventy-one

Ordinalthirteen thousand, four hundred and seventy-first

Scientific notation1.3471 × 10^4

Engineering notation13.471 × 10^3

In other bases

Ternary200110221base 3; the most digit-efficient integer base after e: 9 digits

Quinary412341base 5; one hand: 6 digits

Septenary54163base 7: 5 digits

Nonary20427base 9; each digit is two ternary digits: 5 digits

Duodecimal7967base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1ddbbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:44:31base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T001110T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary111010111100011base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010010011111

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

Bytes234 9f

Gray code10111011010000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010010011111

32-bit00000000000000000011010010011111

64-bit0000000000000000000000000000000000000000000000000011010010011111

One's complement1100101101100000at 16 bits, every bit flipped

Bits reversed1111100100101100at 16 bits

Rotated left by 10110100100111110at 16 bits, wrapping

Shifted left by 1110100100111110= 26,942, no wrap

Shifted right by 11101001001111= 6,735, discarding the low bit

These bits as a double6.65555832 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,477+6

Previous prime13,469−2

Distance to nearest prime2

Nearest square below13,456

Nearest square above13,689

Powers & multiples

13,471 to the power 2181,467,841

13,471 to the power 32,444,553,286,111

13,471 to the power 432,930,577,317,201,281

13,471 to the power 5443,607,807,040,018,456,351

First ten multiples13,471, 26,942, 40,413, 53,884, 67,355, 80,826, 94,297, 107,768, 121,239, 134,710

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 3

Divisible by 5No, remainder 1

Divisible by 6No, remainder 1

Divisible by 7No, remainder 3

Divisible by 8No, remainder 7

Divisible by 9No, remainder 7

Divisible by 10No, remainder 1

Divisible by 11No, remainder 7

Divisible by 12No, remainder 7

Divisible by 100No, remainder 71

Collatz (3n + 1) trajectory

Steps to reach 189the total stopping time

Highest value reached517,91238× the starting value

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

First steps13,471 → 40,414 → 20,207 → 60,622 → 30,311 → 90,934 → 45,467 → 136,402 → 68,201 → 204,604 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,347,100%

13,471% as a decimal134.71

13,471% of 10013,471

13,471% of 1,000134,710

As a fraction of 10013,471/100

Read another way

As seconds3 hours, 44 minutes and 31 seconds

As bytes13.155 KiB

As a 24-bit colour#00349F

Keep nerding

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