Recognised as Number

46,993

Positive
Odd
Prime
5 digits

46,993 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value46,993

Digit count5

Digit sum31

Digit product5,832

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

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation46,993

Distinct prime factors146,993

Number of divisors2

Sum of divisors σ(n)46,994

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)46,992integers below n that share no factor with it

Carmichael function λ(n)46,992the 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, 46,9932 in total

Arithmetic

Previous number46,992

Next number46,994

Double93,986

Half23,496.5

Square2,208,342,049

Cube103,776,617,908,657

Square root216.778688989≈irrational, shown to 9 decimal places

Cube root36.086469097≈

Negation-46,993

Reciprocal0.0000212798≈

Representations

Decimal46,993

Binary101101111001000116 bits

Octal133621

HexadecimalB791

Base 36109D

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

In wordsforty-six thousand, nine hundred and ninety-three

Ordinalforty-six thousand, nine hundred and ninety-third

Scientific notation4.6993 × 10^4

Engineering notation46.993 × 10^3

In other bases

Ternary2101110111base 3; the most digit-efficient integer base after e: 10 digits

Quinary3000433base 5; one hand: 7 digits

Septenary254002base 7: 6 digits

Nonary71414base 9; each digit is two ternary digits: 5 digits

Duodecimal23241base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal5h9dbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal13:3:13base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T101110111digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11100100010010001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1011011110010001

Bit length16 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits7within that length

Bit parityodd9 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes2b7 91

Gray code1110110001011001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1011011110010001

32-bit00000000000000001011011110010001

64-bit0000000000000000000000000000000000000000000000001011011110010001

One's complement0100100001101110at 16 bits, every bit flipped

Bits reversed1000100111101101at 16 bits

Rotated left by 10110111100100011at 16 bits, wrapping

Shifted left by 110110111100100010= 93,986, no wrap

Shifted right by 1101101111001000= 23,496, discarding the low bit

These bits as a double2.32176269 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime46,997+4

Previous prime46,957−36

Distance to nearest prime0, it is prime

Nearest square below46,656

Nearest square above47,089

Powers & multiples

46,993 to the power 22,208,342,049

46,993 to the power 3103,776,617,908,657

46,993 to the power 44,876,774,605,381,518,401

46,993 to the power 5229,174,269,030,693,694,218,193

First ten multiples46,993, 93,986, 140,979, 187,972, 234,965, 281,958, 328,951, 375,944, 422,937, 469,930

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 1

Divisible by 7No, remainder 2

Divisible by 8No, remainder 1

Divisible by 9No, remainder 4

Divisible by 10No, remainder 3

Divisible by 11No, remainder 1

Divisible by 12No, remainder 1

Divisible by 100No, remainder 93

Collatz (3n + 1) trajectory

Steps to reach 157the total stopping time

Highest value reached140,9803× the starting value

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

First steps46,993 → 140,980 → 70,490 → 35,245 → 105,736 → 52,868 → 26,434 → 13,217 → 39,652 → 19,826 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,699,300%

46,993% as a decimal469.93

46,993% of 10046,993

46,993% of 1,000469,930

As a fraction of 10046,993/100

Read another way

As seconds13 hours, 3 minutes and 13 seconds

As bytes45.892 KiB

As a 24-bit colour#00B791

Keep nerding

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