Recognised as Number

13,476

Positive
Even
Composite
5 digits

13,476 is an even 5-digit integer and a composite number. It has 12 divisors and a digital root of 3.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value13,476

Digit count5

Digit sum21

Digit product504

Multiplicative persistence2times the digit product can be taken before one digit is left

Digital root3repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 3 × 1,123

Distinct prime factors32, 3, 1,123

Number of divisors12

Sum of divisors σ(n)31,472

Aliquot sum17,996sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)4,488integers below n that share no factor with it

Carmichael function λ(n)1,122the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 4,488

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 12, 1,123, 2,246, 3,369, 4,492, 6,738, 13,47612 in total

Arithmetic

Previous number13,475

Next number13,477

Double26,952

Half6,738

Square181,602,576

Cube2,447,276,314,176

Square root116.086174887≈irrational, shown to 9 decimal places

Cube root23.796897178≈

Negation-13,476

Reciprocal0.000074206≈

Representations

Decimal13,476

Binary1101001010010014 bits

Octal32244

Hexadecimal34A4

Base 36AEC

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

In wordsthirteen thousand, four hundred and seventy-six

Ordinalthirteen thousand, four hundred and seventy-sixth

Scientific notation1.3476 × 10^4

Engineering notation13.476 × 10^3

In other bases

Ternary200111010base 3; the most digit-efficient integer base after e: 9 digits

Quinary412401base 5; one hand: 6 digits

Septenary54201base 7: 5 digits

Nonary20433base 9; each digit is two ternary digits: 5 digits

Duodecimal7970base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal1ddgbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal3:44:36base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T00111010digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary111010111100100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0011010010100100

Bit length14 bitsto write the magnitude

Set bits6the population count, or Hamming weight

Zero bits8within that length

Bit parityeven6 set bits, so even; not the same as the number itself being even

Highest set bitbit 13worth 8,192

Lowest set bitbit 22 trailing zeros

Power of twoNo

Bytes234 a4

Gray code10111011110110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0011010010100100

32-bit00000000000000000011010010100100

64-bit0000000000000000000000000000000000000000000000000011010010100100

One's complement1100101101011011at 16 bits, every bit flipped

Bits reversed0010010100101100at 16 bits

Rotated left by 10110100101001000at 16 bits, wrapping

Shifted left by 1110100101001000= 26,952, no wrap

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

These bits as a double6.65802864 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime13,477+1

Previous prime13,469−7

Distance to nearest prime1

Nearest square below13,456

Nearest square above13,689

Powers & multiples

13,476 to the power 2181,602,576

13,476 to the power 32,447,276,314,176

13,476 to the power 432,979,495,609,835,776

13,476 to the power 5444,431,682,838,146,917,376

First ten multiples13,476, 26,952, 40,428, 53,904, 67,380, 80,856, 94,332, 107,808, 121,284, 134,760

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 1

Divisible by 6Yes

Divisible by 7No, remainder 1

Divisible by 8No, remainder 4

Divisible by 9No, remainder 3

Divisible by 10No, remainder 6

Divisible by 11No, remainder 1

Divisible by 12Yes

Divisible by 100No, remainder 76

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 steps13,476 → 6,738 → 3,369 → 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 percentage1,347,600%

13,476% as a decimal134.76

13,476% of 10013,476

13,476% of 1,000134,760

As a fraction of 10013,476/100

Read another way

As seconds3 hours, 44 minutes and 36 seconds

As bytes13.16 KiB

As a 24-bit colour#0034A4

Keep nerding

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