Recognised as Number

17,388

Positive
Even
Composite
5 digits

17,388 is an even 5-digit integer and a composite number. It has 48 divisors and a digital root of 9.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value17,388

Digit count5

Digit sum27

Digit product1,344

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root9repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 3^3 × 7 × 23

Distinct prime factors42, 3, 7, 23

Number of divisors48

Sum of divisors σ(n)53,760

Aliquot sum36,372sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)4,752integers below n that share no factor with it

Carmichael function λ(n)198the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 4,752

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 23, 27, 28, 36, 42, 46, 54, 63, 69, 84, 92, 108, 126, 138, 161, 189, 207, 252, 276, 322, 378, 414, 483, 621, 644, 756, 828, 966, 1,242, 1,449, 1,932, 2,484, 2,898, 4,347, 5,796, 8,694, 17,38848 in total

Arithmetic

Previous number17,387

Next number17,389

Double34,776

Half8,694

Square302,342,544

Cube5,257,132,155,072

Square root131.863565855≈irrational, shown to 9 decimal places

Cube root25.906965325≈

Negation-17,388

Reciprocal0.0000575109≈

Representations

Decimal17,388

Binary10000111110110015 bits

Octal41754

Hexadecimal43EC

Base 36DF0

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

In wordsseventeen thousand, three hundred and eighty-eight

Ordinalseventeen thousand, three hundred and eighty-eighth

Scientific notation1.7388 × 10^4

Engineering notation17.388 × 10^3

In other bases

Ternary212212000base 3; the most digit-efficient integer base after e: 9 digits

Quinary1024023base 5; one hand: 7 digits

Septenary101460base 7: 6 digits

Nonary25760base 9; each digit is two ternary digits: 5 digits

Duodecimala090base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal2398base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal4:49:48base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary10T00TT000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100010000111100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0100001111101100

Bit length15 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits7within that length

Bit parityeven8 set bits, so even; not the same as the number itself being even

Highest set bitbit 14worth 16,384

Lowest set bitbit 22 trailing zeros

Power of twoNo

Bytes243 ec

Gray code110001000011010n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0100001111101100

32-bit00000000000000000100001111101100

64-bit0000000000000000000000000000000000000000000000000100001111101100

One's complement1011110000010011at 16 bits, every bit flipped

Bits reversed0011011111000010at 16 bits

Rotated left by 11000011111011000at 16 bits, wrapping

Shifted left by 11000011111011000= 34,776, no wrap

Shifted right by 110000111110110= 8,694, discarding the low bit

These bits as a double8.59081345 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime17,389+1

Previous prime17,387−1

Distance to nearest prime1

Nearest square below17,161

Nearest square above17,424

Powers & multiples

17,388 to the power 2302,342,544

17,388 to the power 35,257,132,155,072

17,388 to the power 491,411,013,912,391,936

17,388 to the power 51,589,454,709,908,670,983,168

First ten multiples17,388, 34,776, 52,164, 69,552, 86,940, 104,328, 121,716, 139,104, 156,492, 173,880

Powers of twoBetween 2^14 (16,384) and 2^15 (32,768)

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 3

Divisible by 6Yes

Divisible by 7Yes

Divisible by 8No, remainder 4

Divisible by 9Yes

Divisible by 10No, remainder 8

Divisible by 11No, remainder 8

Divisible by 12Yes

Divisible by 100No, remainder 88

Collatz (3n + 1) trajectory

Steps to reach 1185the total stopping time

Highest value reached225,98812× the starting value

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

First steps17,388 → 8,694 → 4,347 → 13,042 → 6,521 → 19,564 → 9,782 → 4,891 → 14,674 → 7,337 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,738,800%

17,388% as a decimal173.88

17,388% of 10017,388

17,388% of 1,000173,880

As a fraction of 10017,388/100

Read another way

As seconds4 hours, 49 minutes and 48 seconds

As bytes16.98 KiB

As a 24-bit colour#0043EC

Keep nerding

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