Recognised as Number

72,013

Positive
Odd
Composite
5 digits

72,013 is an odd 5-digit integer and a composite number. It has 8 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value72,013

Digit count5

Digit sum13

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times 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 factorisation23 × 31 × 101

Distinct prime factors323, 31, 101

Number of divisors8

Sum of divisors σ(n)78,336

Aliquot sum6,323sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)66,000integers below n that share no factor with it

Carmichael function λ(n)3,300the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 66,000

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

SquarefreeYesno repeated prime factor

All divisors1, 23, 31, 101, 713, 2,323, 3,131, 72,0138 in total

Arithmetic

Previous number72,012

Next number72,014

Double144,026

Half36,006.5

Square5,185,872,169

Cube373,450,212,506,197

Square root268.352380276≈irrational, shown to 9 decimal places

Cube root41.604180115≈

Negation-72,013

Reciprocal0.0000138864≈

Representations

Decimal72,013

Binary1000110010100110117 bits

Octal214515

Hexadecimal1194D

Base 361JKD

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

In wordsseventy-two thousand and thirteen

Ordinalseventy-two thousand and thirteenth

Scientific notation7.2013 × 10^4

Engineering notation72.013 × 10^3

In other bases

Ternary10122210011base 3; the most digit-efficient integer base after e: 11 digits

Quinary4301023base 5; one hand: 7 digits

Septenary416644base 7: 6 digits

Nonary118704base 9; each digit is two ternary digits: 6 digits

Duodecimal35811base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal900dbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal20:0:13base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary11T00T10011digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary10110100101011101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000000010001100101001101

Bit length17 bitsto write the magnitude

Set bits8the population count, or Hamming weight

Zero bits9within that length

Bit parityeven8 set bits, so even; 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 19 4d

Gray code11001010111101011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000000010001100101001101

64-bit0000000000000000000000000000000000000000000000010001100101001101

One's complement11111111111111101110011010110010at 32 bits, every bit flipped

Bits reversed10110010100110001000000000000000at 32 bits

Rotated left by 100000000000000100011001010011010at 32 bits, wrapping

Shifted left by 1100011001010011010= 144,026, no wrap

Shifted right by 11000110010100110= 36,006, discarding the low bit

These bits as a double3.55791494 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime72,019+6

Previous prime71,999−14

Distance to nearest prime6

Nearest square below71,824

Nearest square above72,361

Powers & multiples

72,013 to the power 25,185,872,169

72,013 to the power 3373,450,212,506,197

72,013 to the power 426,893,270,153,208,764,561

72,013 to the power 51,936,665,063,543,022,762,331,293

First ten multiples72,013, 144,026, 216,039, 288,052, 360,065, 432,078, 504,091, 576,104, 648,117, 720,130

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

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 4

Divisible by 8No, remainder 5

Divisible by 9No, remainder 4

Divisible by 10No, remainder 3

Divisible by 11No, remainder 7

Divisible by 12No, remainder 1

Divisible by 100No, remainder 13

Collatz (3n + 1) trajectory

Steps to reach 1143the total stopping time

Highest value reached216,0403× the starting value

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

First steps72,013 → 216,040 → 108,020 → 54,010 → 27,005 → 81,016 → 40,508 → 20,254 → 10,127 → 30,382 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage7,201,300%

72,013% as a decimal720.13

72,013% of 10072,013

72,013% of 1,000720,130

As a fraction of 10072,013/100

Read another way

As seconds20 hours and 13 seconds

As bytes70.325 KiB

As a 24-bit colour#01194D

Keep nerding

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