Recognised as Number

38,400

Positive
Even
Composite
5 digits

38,400 is an even 5-digit integer and a composite number. It has 60 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value38,400

Digit count5

Digit sum15

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times 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 numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^9 × 3 × 5^2

Distinct prime factors32, 3, 5

Number of divisors60

Sum of divisors σ(n)126,852

Aliquot sum88,452sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)10,240integers below n that share no factor with it

Carmichael function λ(n)640the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 10,240

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 32, 40, 48, 50, 60, 64, 75, 80, 96, 100, 120, 128, 150, 160, 192, 200, 240, 256, 300, 320, 384, 400, 480, 512, 600, 640, 768, 800, 960, 1,200, 1,280, 1,536, 1,600, 1,920, 2,400, 2,560, 3,200, 3,840, 4,800, 6,400, 7,680, 9,600, 12,800, 19,200, 38,40060 in total

Arithmetic

Previous number38,399

Next number38,401

Double76,800

Half19,200

Square1,474,560,000

Cube56,623,104,000,000

Square root195.959179423≈irrational, shown to 9 decimal places

Cube root33.737306612≈

Negation-38,400

Reciprocal0.0000260417≈

Representations

Decimal38,400

Binary100101100000000016 bits

Octal113000

Hexadecimal9600

Base 36TMO

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

In wordsthirty-eight thousand, four hundred

Ordinalthirty-eight thousand, four hundredth

Scientific notation3.84 × 10^4

Engineering notation38.4 × 10^3

In other bases

Ternary1221200020base 3; the most digit-efficient integer base after e: 10 digits

Quinary2212100base 5; one hand: 7 digits

Septenary216645base 7: 6 digits

Nonary57606base 9; each digit is two ternary digits: 5 digits

Duodecimal1a280base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal4g00base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal10:40:0base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T00TT001T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110101000000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1001011000000000

Bit length16 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits12within that length

Bit parityeven4 set bits, so even; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 99 trailing zeros

Power of twoNo

Bytes296 00

Gray code1101110100000000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1001011000000000

32-bit00000000000000001001011000000000

64-bit0000000000000000000000000000000000000000000000001001011000000000

One's complement0110100111111111at 16 bits, every bit flipped

Bits reversed0000000001101001at 16 bits

Rotated left by 10010110000000001at 16 bits, wrapping

Shifted left by 110010110000000000= 76,800, no wrap

Shifted right by 1100101100000000= 19,200, discarding the low bit

These bits as a double1.89721208 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime38,431+31

Previous prime38,393−7

Distance to nearest prime7

Nearest square below38,025

Nearest square above38,416

Powers & multiples

38,400 to the power 21,474,560,000

38,400 to the power 356,623,104,000,000

38,400 to the power 42,174,327,193,600,000,000

38,400 to the power 583,494,164,234,240,000,000,000

First ten multiples38,400, 76,800, 115,200, 153,600, 192,000, 230,400, 268,800, 307,200, 345,600, 384,000

Powers of twoBetween 2^15 (32,768) and 2^16 (65,536)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6Yes

Divisible by 7No, remainder 5

Divisible by 8Yes

Divisible by 9No, remainder 6

Divisible by 10Yes

Divisible by 11No, remainder 10

Divisible by 12Yes

Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 123the total stopping time

Highest value reached38,400

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

First steps38,400 → 19,200 → 9,600 → 4,800 → 2,400 → 1,200 → 600 → 300 → 150 → 75 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,840,000%

38,400% as a decimal384

38,400% of 10038,400

38,400% of 1,000384,000

As a fraction of 10038,400/100

Read another way

As seconds10 hours and 40 minutes

As bytes37.5 KiB

As a 24-bit colour#009600

Keep nerding

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