Recognised as Number

49,988

Positive
Even
Composite
5 digits

49,988 is an even 5-digit integer and a composite number. It has 6 divisors and a digital root of 2.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value49,988

Digit count5

Digit sum38

Digit product20,736

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

Digital root2repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^2 × 12,497

Distinct prime factors22, 12,497

Number of divisors6

Sum of divisors σ(n)87,486

Aliquot sum37,498sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)24,992integers below n that share no factor with it

Carmichael function λ(n)12,496the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 24,992

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 4, 12,497, 24,994, 49,9886 in total

Arithmetic

Previous number49,987

Next number49,989

Double99,976

Half24,994

Square2,498,800,144

Cube124,910,021,598,272

Square root223.579963324≈irrational, shown to 9 decimal places

Cube root36.837367525≈

Negation-49,988

Reciprocal0.0000200048≈

Representations

Decimal49,988

Binary110000110100010016 bits

Octal141504

HexadecimalC344

Base 3612KK

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

In wordsforty-nine thousand, nine hundred and eighty-eight

Ordinalforty-nine thousand, nine hundred and eighty-eighth

Scientific notation4.9988 × 10^4

Engineering notation49.988 × 10^3

In other bases

Ternary2112120102base 3; the most digit-efficient integer base after e: 10 digits

Quinary3044423base 5; one hand: 7 digits

Septenary265511base 7: 6 digits

Nonary75512base 9; each digit is two ternary digits: 5 digits

Duodecimal24b18base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal64j8base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal13:53:8base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary10TT0TT011Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11100011101000100base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1100001101000100

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 22 trailing zeros

Power of twoNo

Bytes2c3 44

Gray code1010001011100110n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1100001101000100

32-bit00000000000000001100001101000100

64-bit0000000000000000000000000000000000000000000000001100001101000100

One's complement0011110010111011at 16 bits, every bit flipped

Bits reversed0010001011000011at 16 bits

Rotated left by 11000011010001001at 16 bits, wrapping

Shifted left by 111000011010001000= 99,976, no wrap

Shifted right by 1110000110100010= 24,994, discarding the low bit

These bits as a double2.46973535 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime49,991+3

Previous prime49,957−31

Distance to nearest prime3

Nearest square below49,729

Nearest square above50,176

Powers & multiples

49,988 to the power 22,498,800,144

49,988 to the power 3124,910,021,598,272

49,988 to the power 46,244,002,159,654,420,736

49,988 to the power 5312,125,179,956,805,183,751,168

First ten multiples49,988, 99,976, 149,964, 199,952, 249,940, 299,928, 349,916, 399,904, 449,892, 499,880

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

Divisibility tests

Divisible by 2Yes

Divisible by 3No, remainder 2

Divisible by 4Yes

Divisible by 5No, remainder 3

Divisible by 6No, remainder 2

Divisible by 7No, remainder 1

Divisible by 8No, remainder 4

Divisible by 9No, remainder 2

Divisible by 10No, remainder 8

Divisible by 11No, remainder 4

Divisible by 12No, remainder 8

Divisible by 100No, remainder 88

Collatz (3n + 1) trajectory

Steps to reach 1158the total stopping time

Highest value reached49,988

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

First steps49,988 → 24,994 → 12,497 → 37,492 → 18,746 → 9,373 → 28,120 → 14,060 → 7,030 → 3,515 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,998,800%

49,988% as a decimal499.88

49,988% of 10049,988

49,988% of 1,000499,880

As a fraction of 10049,988/100

Read another way

As seconds13 hours, 53 minutes and 8 seconds

As bytes48.816 KiB

As a 24-bit colour#00C344

Keep nerding

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