Recognised as Number

77,073

Positive
Odd
Composite
5 digits

77,073 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 6.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value77,073

Digit count5

Digit sum24

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 numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation3 × 23 × 1,117

Distinct prime factors33, 23, 1,117

Number of divisors8

Sum of divisors σ(n)107,328

Aliquot sum30,255sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)49,104integers below n that share no factor with it

Carmichael function λ(n)12,276the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 49,104

Möbius function μ(n)−13 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 23, 69, 1,117, 3,351, 25,691, 77,0738 in total

Arithmetic

Previous number77,072

Next number77,074

Double154,146

Half38,536.5

Square5,940,247,329

Cube457,832,682,388,017

Square root277.620244219≈irrational, shown to 9 decimal places

Cube root42.556648795≈

Negation-77,073

Reciprocal0.0000129747≈

Representations

Decimal77,073

Binary1001011010001000117 bits

Octal226421

Hexadecimal12D11

Base 361NGX

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

In wordsseventy-seven thousand and seventy-three

Ordinalseventy-seven thousand and seventy-third

Scientific notation7.7073 × 10^4

Engineering notation77.073 × 10^3

In other bases

Ternary10220201120base 3; the most digit-efficient integer base after e: 11 digits

Quinary4431243base 5; one hand: 7 digits

Septenary440463base 7: 6 digits

Nonary126646base 9; each digit is two ternary digits: 6 digits

Duodecimal38729base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal9cddbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal21:24:33base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary110T1T1TTT0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary10111110100010001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000000010010110100010001

Bit length17 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits10within that length

Bit parityodd7 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 16worth 65,536

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes301 2d 11

Gray code11011101110011001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000000010010110100010001

64-bit0000000000000000000000000000000000000000000000010010110100010001

One's complement11111111111111101101001011101110at 32 bits, every bit flipped

Bits reversed10001000101101001000000000000000at 32 bits

Rotated left by 100000000000000100101101000100010at 32 bits, wrapping

Shifted left by 1100101101000100010= 154,146, no wrap

Shifted right by 11001011010001000= 38,536, discarding the low bit

These bits as a double3.80791215 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime77,081+8

Previous prime77,069−4

Distance to nearest prime4

Nearest square below76,729

Nearest square above77,284

Powers & multiples

77,073 to the power 25,940,247,329

77,073 to the power 3457,832,682,388,017

77,073 to the power 435,286,538,329,691,634,241

77,073 to the power 52,719,639,368,684,323,325,856,593

First ten multiples77,073, 154,146, 231,219, 308,292, 385,365, 462,438, 539,511, 616,584, 693,657, 770,730

Powers of twoBetween 2^16 (65,536) and 2^17 (131,072)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3Yes

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 3

Divisible by 7No, remainder 3

Divisible by 8No, remainder 1

Divisible by 9No, remainder 6

Divisible by 10No, remainder 3

Divisible by 11No, remainder 7

Divisible by 12No, remainder 9

Divisible by 100No, remainder 73

Collatz (3n + 1) trajectory

Steps to reach 150the total stopping time

Highest value reached231,2203× the starting value

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

First steps77,073 → 231,220 → 115,610 → 57,805 → 173,416 → 86,708 → 43,354 → 21,677 → 65,032 → 32,516 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage7,707,300%

77,073% as a decimal770.73

77,073% of 10077,073

77,073% of 1,000770,730

As a fraction of 10077,073/100

Read another way

As seconds21 hours, 24 minutes and 33 seconds

As bytes75.267 KiB

As a 24-bit colour#012D11

Keep nerding

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