Recognised as Number

42,315

Positive
Odd
Composite
5 digits

42,315 is an odd 5-digit integer and a composite number. It has 32 divisors and a digital root of 6.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value42,315

Digit count5

Digit sum15

Digit product120

Multiplicative persistence2times 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 numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation3 × 5 × 7 × 13 × 31

Distinct prime factors53, 5, 7, 13, 31

Number of divisors32

Sum of divisors σ(n)86,016

Aliquot sum43,701sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)17,280integers below n that share no factor with it

Carmichael function λ(n)60the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 17,280

Möbius function μ(n)−15 distinct prime factors, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 3, 5, 7, 13, 15, 21, 31, 35, 39, 65, 91, 93, 105, 155, 195, 217, 273, 403, 455, 465, 651, 1,085, 1,209, 1,365, 2,015, 2,821, 3,255, 6,045, 8,463, 14,105, 42,31532 in total

Arithmetic

Previous number42,314

Next number42,316

Double84,630

Half21,157.5

Square1,790,559,225

Cube75,767,513,605,875

Square root205.706101028≈irrational, shown to 9 decimal places

Cube root34.846950764≈

Negation-42,315

Reciprocal0.0000236323≈

Representations

Decimal42,315

Binary101001010100101116 bits

Octal122513

HexadecimalA54B

Base 36WNF

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

In wordsforty-two thousand, three hundred and fifteen

Ordinalforty-two thousand, three hundred and fifteenth

Scientific notation4.2315 × 10^4

Engineering notation42.315 × 10^3

In other bases

Ternary2011001020base 3; the most digit-efficient integer base after e: 10 digits

Quinary2323230base 5; one hand: 7 digits

Septenary234240base 7: 6 digits

Nonary64036base 9; each digit is two ternary digits: 5 digits

Duodecimal205a3base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal55ffbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:45:15base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0110011T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110010101011111base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1010010101001011

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

Bytes2a5 4b

Gray code1111011111101110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1010010101001011

32-bit00000000000000001010010101001011

64-bit0000000000000000000000000000000000000000000000001010010101001011

One's complement0101101010110100at 16 bits, every bit flipped

Bits reversed1101001010100101at 16 bits

Rotated left by 10100101010010111at 16 bits, wrapping

Shifted left by 110100101010010110= 84,630, no wrap

Shifted right by 1101001010100101= 21,157, discarding the low bit

These bits as a double2.09063878 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime42,323+8

Previous prime42,307−8

Distance to nearest prime8

Nearest square below42,025

Nearest square above42,436

Powers & multiples

42,315 to the power 21,790,559,225

42,315 to the power 375,767,513,605,875

42,315 to the power 43,206,102,338,232,600,625

42,315 to the power 5135,666,220,442,312,495,446,875

First ten multiples42,315, 84,630, 126,945, 169,260, 211,575, 253,890, 296,205, 338,520, 380,835, 423,150

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 3

Divisible by 5Yes

Divisible by 6No, remainder 3

Divisible by 7Yes

Divisible by 8No, remainder 3

Divisible by 9No, remainder 6

Divisible by 10No, remainder 5

Divisible by 11No, remainder 9

Divisible by 12No, remainder 3

Divisible by 100No, remainder 15

Collatz (3n + 1) trajectory

Steps to reach 157the total stopping time

Highest value reached190,4204× the starting value

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

First steps42,315 → 126,946 → 63,473 → 190,420 → 95,210 → 47,605 → 142,816 → 71,408 → 35,704 → 17,852 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,231,500%

42,315% as a decimal423.15

42,315% of 10042,315

42,315% of 1,000423,150

As a fraction of 10042,315/100

Read another way

As seconds11 hours, 45 minutes and 15 seconds

As bytes41.323 KiB

As a 24-bit colour#00A54B

Keep nerding

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