Recognised as Number

42,072

Positive
Even
Composite
5 digits

42,072 is an even 5-digit integer and a composite number. It has 16 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value42,072

Digit count5

Digit sum15

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 factorisation2^3 × 3 × 1,753

Distinct prime factors32, 3, 1,753

Number of divisors16

Sum of divisors σ(n)105,240

Aliquot sum63,168sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)14,016integers below n that share no factor with it

Carmichael function λ(n)1,752the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 14,016

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 8, 12, 24, 1,753, 3,506, 5,259, 7,012, 10,518, 14,024, 21,036, 42,07216 in total

Arithmetic

Previous number42,071

Next number42,073

Double84,144

Half21,036

Square1,770,053,184

Cube74,469,677,557,248

Square root205.114602113≈irrational, shown to 9 decimal places

Cube root34.780118119≈

Negation-42,072

Reciprocal0.0000237688≈

Representations

Decimal42,072

Binary101001000101100016 bits

Octal122130

HexadecimalA458

Base 36WGO

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

In wordsforty-two thousand and seventy-two

Ordinalforty-two thousand and seventy-second

Scientific notation4.2072 × 10^4

Engineering notation42.072 × 10^3

In other bases

Ternary2010201020base 3; the most digit-efficient integer base after e: 10 digits

Quinary2321242base 5; one hand: 7 digits

Septenary233442base 7: 6 digits

Nonary63636base 9; each digit is two ternary digits: 5 digits

Duodecimal20420base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal553cbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:41:12base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T011T011T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110010110101000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1010010001011000

Bit length16 bitsto write the magnitude

Set bits6the population count, or Hamming weight

Zero bits10within that length

Bit parityeven6 set bits, so even; not the same as the number itself being even

Highest set bitbit 15worth 32,768

Lowest set bitbit 33 trailing zeros

Power of twoNo

Bytes2a4 58

Gray code1111011001110100n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1010010001011000

32-bit00000000000000001010010001011000

64-bit0000000000000000000000000000000000000000000000001010010001011000

One's complement0101101110100111at 16 bits, every bit flipped

Bits reversed0001101000100101at 16 bits

Rotated left by 10100100010110001at 16 bits, wrapping

Shifted left by 110100100010110000= 84,144, no wrap

Shifted right by 1101001000101100= 21,036, discarding the low bit

These bits as a double2.07863299 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime42,073+1

Previous prime42,071−1

Distance to nearest prime1

Nearest square below42,025

Nearest square above42,436

Powers & multiples

42,072 to the power 21,770,053,184

42,072 to the power 374,469,677,557,248

42,072 to the power 43,133,088,274,188,537,856

42,072 to the power 5131,815,289,871,660,164,677,632

First ten multiples42,072, 84,144, 126,216, 168,288, 210,360, 252,432, 294,504, 336,576, 378,648, 420,720

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5No, remainder 2

Divisible by 6Yes

Divisible by 7No, remainder 2

Divisible by 8Yes

Divisible by 9No, remainder 6

Divisible by 10No, remainder 2

Divisible by 11No, remainder 8

Divisible by 12Yes

Divisible by 100No, remainder 72

Collatz (3n + 1) trajectory

Steps to reach 1106the total stopping time

Highest value reached42,072

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

First steps42,072 → 21,036 → 10,518 → 5,259 → 15,778 → 7,889 → 23,668 → 11,834 → 5,917 → 17,752 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,207,200%

42,072% as a decimal420.72

42,072% of 10042,072

42,072% of 1,000420,720

As a fraction of 10042,072/100

Read another way

As seconds11 hours, 41 minutes and 12 seconds

As bytes41.086 KiB

As a 24-bit colour#00A458

Keep nerding

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