Recognised as Number

42,976

Positive
Even
Composite
5 digits

42,976 is an even 5-digit integer and a composite number. It has 24 divisors and a digital root of 1.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value42,976

Digit count5

Digit sum28

Digit product3,024

Multiplicative persistence2times the digit product can be taken before one digit is left

Digital root1repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^5 × 17 × 79

Distinct prime factors32, 17, 79

Number of divisors24

Sum of divisors σ(n)90,720

Aliquot sum47,744sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)19,968integers below n that share no factor with it

Carmichael function λ(n)624the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 19,968

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 8, 16, 17, 32, 34, 68, 79, 136, 158, 272, 316, 544, 632, 1,264, 1,343, 2,528, 2,686, 5,372, 10,744, 21,488, 42,97624 in total

Arithmetic

Previous number42,975

Next number42,977

Double85,952

Half21,488

Square1,846,936,576

Cube79,373,946,290,176

Square root207.306536318≈irrational, shown to 9 decimal places

Cube root35.027461441≈

Negation-42,976

Reciprocal0.0000232688≈

Representations

Decimal42,976

Binary101001111110000016 bits

Octal123740

HexadecimalA7E0

Base 36X5S

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

In wordsforty-two thousand, nine hundred and seventy-six

Ordinalforty-two thousand, nine hundred and seventy-sixth

Scientific notation4.2976 × 10^4

Engineering notation42.976 × 10^3

In other bases

Ternary2011221201base 3; the most digit-efficient integer base after e: 10 digits

Quinary2333401base 5; one hand: 7 digits

Septenary236203base 7: 6 digits

Nonary64851base 9; each digit is two ternary digits: 5 digits

Duodecimal20a54base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal578gbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:56:16base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T1TT00TT01digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11111100000100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1010011111100000

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 even

Highest set bitbit 15worth 32,768

Lowest set bitbit 55 trailing zeros

Power of twoNo

Bytes2a7 e0

Gray code1111010000010000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1010011111100000

32-bit00000000000000001010011111100000

64-bit0000000000000000000000000000000000000000000000001010011111100000

One's complement0101100000011111at 16 bits, every bit flipped

Bits reversed0000011111100101at 16 bits

Rotated left by 10100111111000001at 16 bits, wrapping

Shifted left by 110100111111000000= 85,952, no wrap

Shifted right by 1101001111110000= 21,488, discarding the low bit

These bits as a double2.12329652 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime42,979+3

Previous prime42,967−9

Distance to nearest prime3

Nearest square below42,849

Nearest square above43,264

Powers & multiples

42,976 to the power 21,846,936,576

42,976 to the power 379,373,946,290,176

42,976 to the power 43,411,174,715,766,603,776

42,976 to the power 5146,598,644,584,785,563,877,376

First ten multiples42,976, 85,952, 128,928, 171,904, 214,880, 257,856, 300,832, 343,808, 386,784, 429,760

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

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 1

Divisible by 4Yes

Divisible by 5No, remainder 1

Divisible by 6No, remainder 4

Divisible by 7No, remainder 3

Divisible by 8Yes

Divisible by 9No, remainder 1

Divisible by 10No, remainder 6

Divisible by 11No, remainder 10

Divisible by 12No, remainder 4

Divisible by 100No, remainder 76

Collatz (3n + 1) trajectory

Steps to reach 1101the total stopping time

Highest value reached42,976

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

First steps42,976 → 21,488 → 10,744 → 5,372 → 2,686 → 1,343 → 4,030 → 2,015 → 6,046 → 3,023 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,297,600%

42,976% as a decimal429.76

42,976% of 10042,976

42,976% of 1,000429,760

As a fraction of 10042,976/100

Read another way

As seconds11 hours, 56 minutes and 16 seconds

As bytes41.969 KiB

As a 24-bit colour#00A7E0

Keep nerding

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