Recognised as Number

90,042

Positive
Even
Composite
5 digits

90,042 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 value90,042

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 × 43 × 349

Distinct prime factors42, 3, 43, 349

Number of divisors16

Sum of divisors σ(n)184,800

Aliquot sum94,758sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)29,232integers below n that share no factor with it

Carmichael function λ(n)2,436the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 29,232

Möbius function μ(n)+14 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 2, 3, 6, 43, 86, 129, 258, 349, 698, 1,047, 2,094, 15,007, 30,014, 45,021, 90,04216 in total

Arithmetic

Previous number90,041

Next number90,043

Double180,084

Half45,021

Square8,107,561,764

Cube730,021,076,354,088

Square root300.069991835≈irrational, shown to 9 decimal places

Cube root44.821017456≈

Negation-90,042

Reciprocal0.0000111059≈

Representations

Decimal90,042

Binary1010111111011101017 bits

Octal257672

Hexadecimal15FBA

Base 361XH6

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

In wordsninety thousand and forty-two

Ordinalninety thousand and forty-second

Scientific notation9.0042 × 10^4

Engineering notation90.042 × 10^3

In other bases

Ternary11120111220base 3; the most digit-efficient integer base after e: 11 digits

Quinary10340132base 5; one hand: 8 digits

Septenary523341base 7: 6 digits

Nonary146456base 9; each digit is two ternary digits: 6 digits

Duodecimal44136base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimalb522base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal25:0:42base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TTTT1TTT0T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary1101010000011001110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000000010101111110111010

Bit length17 bitsto write the magnitude

Set bits12the population count, or Hamming weight

Zero bits5within that length

Bit parityeven12 set bits, so even; not the same as the number itself being even

Highest set bitbit 16worth 65,536

Lowest set bitbit 11 trailing zero

Power of twoNo

Bytes301 5f ba

Gray code11111000001100111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000000010101111110111010

64-bit0000000000000000000000000000000000000000000000010101111110111010

One's complement11111111111111101010000001000101at 32 bits, every bit flipped

Bits reversed01011101111110101000000000000000at 32 bits

Rotated left by 100000000000000101011111101110100at 32 bits, wrapping

Shifted left by 1101011111101110100= 180,084, no wrap

Shifted right by 11010111111011101= 45,021, discarding the low bit

These bits as a double4.44866589 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime90,053+11

Previous prime90,031−11

Distance to nearest prime11

Nearest square below90,000

Nearest square above90,601

Powers & multiples

90,042 to the power 28,107,561,764

90,042 to the power 3730,021,076,354,088

90,042 to the power 465,732,557,757,074,791,696

90,042 to the power 55,918,690,965,562,528,393,891,232

First ten multiples90,042, 180,084, 270,126, 360,168, 450,210, 540,252, 630,294, 720,336, 810,378, 900,420

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4No, remainder 2

Divisible by 5No, remainder 2

Divisible by 6Yes

Divisible by 7No, remainder 1

Divisible by 8No, remainder 2

Divisible by 9No, remainder 6

Divisible by 10No, remainder 2

Divisible by 11No, remainder 7

Divisible by 12No, remainder 6

Divisible by 100No, remainder 42

Collatz (3n + 1) trajectory

Steps to reach 163the total stopping time

Highest value reached135,0641× the starting value

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

First steps90,042 → 45,021 → 135,064 → 67,532 → 33,766 → 16,883 → 50,650 → 25,325 → 75,976 → 37,988 → …

Last steps… → 32 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage9,004,200%

90,042% as a decimal900.42

90,042% of 10090,042

90,042% of 1,000900,420

As a fraction of 10090,042/100

Read another way

As seconds1 day, 1 hour and 42 seconds

As bytes87.932 KiB

As a 24-bit colour#015FBA

Keep nerding

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