Recognised as Number

40,041

Positive
Odd
Composite
5 digits

40,041 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 9.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value40,041

Digit count5

Digit sum9

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times 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 factorisation3^3 × 1,483

Distinct prime factors23, 1,483

Number of divisors8

Sum of divisors σ(n)59,360

Aliquot sum19,319sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)26,676integers below n that share no factor with it

Carmichael function λ(n)4,446the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 26,676

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

SquarefreeNohas a repeated prime factor

All divisors1, 3, 9, 27, 1,483, 4,449, 13,347, 40,0418 in total

Arithmetic

Previous number40,040

Next number40,042

Double80,082

Half20,020.5

Square1,603,281,681

Cube64,197,001,788,921

Square root200.102473748≈irrational, shown to 9 decimal places

Cube root34.211199779≈

Negation-40,041

Reciprocal0.0000249744≈

Representations

Decimal40,041

Binary100111000110100116 bits

Octal116151

Hexadecimal9C69

Base 36UW9

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

In wordsforty thousand and forty-one

Ordinalforty thousand and forty-first

Scientific notation4.0041 × 10^4

Engineering notation40.041 × 10^3

In other bases

Ternary2000221000base 3; the most digit-efficient integer base after e: 10 digits

Quinary2240131base 5; one hand: 7 digits

Septenary224511base 7: 6 digits

Nonary60830base 9; each digit is two ternary digits: 5 digits

Duodecimal1b209base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal5021base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:7:21base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0010T1000digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110110110111001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1001110001101001

Bit length16 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits8within that length

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

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes29c 69

Gray code1101001001011101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1001110001101001

32-bit00000000000000001001110001101001

64-bit0000000000000000000000000000000000000000000000001001110001101001

One's complement0110001110010110at 16 bits, every bit flipped

Bits reversed1001011000111001at 16 bits

Rotated left by 10011100011010011at 16 bits, wrapping

Shifted left by 110011100011010010= 80,082, no wrap

Shifted right by 1100111000110100= 20,020, discarding the low bit

These bits as a double1.97828825 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime40,063+22

Previous prime40,039−2

Distance to nearest prime2

Nearest square below40,000

Nearest square above40,401

Powers & multiples

40,041 to the power 21,603,281,681

40,041 to the power 364,197,001,788,921

40,041 to the power 42,570,512,148,630,185,761

40,041 to the power 5102,925,876,943,301,268,056,201

First ten multiples40,041, 80,082, 120,123, 160,164, 200,205, 240,246, 280,287, 320,328, 360,369, 400,410

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 1

Divisible by 5No, remainder 1

Divisible by 6No, remainder 3

Divisible by 7No, remainder 1

Divisible by 8No, remainder 1

Divisible by 9Yes

Divisible by 10No, remainder 1

Divisible by 11No, remainder 1

Divisible by 12No, remainder 9

Divisible by 100No, remainder 41

Collatz (3n + 1) trajectory

Steps to reach 1106the total stopping time

Highest value reached410,99210× the starting value

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

First steps40,041 → 120,124 → 60,062 → 30,031 → 90,094 → 45,047 → 135,142 → 67,571 → 202,714 → 101,357 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,004,100%

40,041% as a decimal400.41

40,041% of 10040,041

40,041% of 1,000400,410

As a fraction of 10040,041/100

Read another way

As seconds11 hours, 7 minutes and 21 seconds

As bytes39.103 KiB

As a 24-bit colour#009C69

Keep nerding

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