Recognised as Number

16,673

Positive
Odd
Prime
5 digits

16,673 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 5.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value16,673

Digit count5

Digit sum23

Digit product756

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

Digital root5repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation16,673

Distinct prime factors116,673

Number of divisors2

Sum of divisors σ(n)16,674

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)16,672integers below n that share no factor with it

Carmichael function λ(n)16,672the 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, 16,6732 in total

Arithmetic

Previous number16,672

Next number16,674

Double33,346

Half8,336.5

Square277,988,929

Cube4,634,909,413,217

Square root129.123971438≈irrational, shown to 9 decimal places

Cube root25.546882865≈

Negation-16,673

Reciprocal0.0000599772≈

Representations

Decimal16,673

Binary10000010010000115 bits

Octal40441

Hexadecimal4121

Base 36CV5

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

In wordssixteen thousand, six hundred and seventy-three

Ordinalsixteen thousand, six hundred and seventy-third

Scientific notation1.6673 × 10^4

Engineering notation16.673 × 10^3

In other bases

Ternary211212112base 3; the most digit-efficient integer base after e: 9 digits

Quinary1013143base 5; one hand: 7 digits

Septenary66416base 7: 5 digits

Nonary24775base 9; each digit is two ternary digits: 5 digits

Duodecimal9795base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 4 digits

Vigesimal21ddbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal4:37:53base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary10TT0T0TTTdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary100000101100001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

0100000100100001

Bit length15 bitsto write the magnitude

Set bits4the population count, or Hamming weight

Zero bits11within that length

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

Highest set bitbit 14worth 16,384

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes241 21

Gray code110000110110001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit0100000100100001

32-bit00000000000000000100000100100001

64-bit0000000000000000000000000000000000000000000000000100000100100001

One's complement1011111011011110at 16 bits, every bit flipped

Bits reversed1000010010000010at 16 bits

Rotated left by 11000001001000010at 16 bits, wrapping

Shifted left by 11000001001000010= 33,346, no wrap

Shifted right by 110000010010000= 8,336, discarding the low bit

These bits as a double8.23755651 × 10^-320≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime16,691+18

Previous prime16,661−12

Distance to nearest prime0, it is prime

Nearest square below16,641

Nearest square above16,900

Powers & multiples

16,673 to the power 2277,988,929

16,673 to the power 34,634,909,413,217

16,673 to the power 477,277,844,646,567,041

16,673 to the power 51,288,453,503,792,212,274,593

First ten multiples16,673, 33,346, 50,019, 66,692, 83,365, 100,038, 116,711, 133,384, 150,057, 166,730

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 5

Divisible by 7No, remainder 6

Divisible by 8No, remainder 1

Divisible by 9No, remainder 5

Divisible by 10No, remainder 3

Divisible by 11No, remainder 8

Divisible by 12No, remainder 5

Divisible by 100No, remainder 73

Collatz (3n + 1) trajectory

Steps to reach 1159the total stopping time

Highest value reached50,0203× the starting value

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

First steps16,673 → 50,020 → 25,010 → 12,505 → 37,516 → 18,758 → 9,379 → 28,138 → 14,069 → 42,208 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage1,667,300%

16,673% as a decimal166.73

16,673% of 10016,673

16,673% of 1,000166,730

As a fraction of 10016,673/100

Read another way

As seconds4 hours, 37 minutes and 53 seconds

As bytes16.282 KiB

As a 24-bit colour#004121

Keep nerding

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