Recognised as Number

37,489

Positive
Odd
Prime
5 digits

37,489 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 4.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value37,489

Digit count5

Digit sum31

Digit product6,048

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

Digital root4repeated digit sum

PalindromicNoreads differently backwards

Happy numberYessquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation37,489

Distinct prime factors137,489

Number of divisors2

Sum of divisors σ(n)37,490

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)37,488integers below n that share no factor with it

Carmichael function λ(n)37,488the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)−11 distinct prime factor, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 37,4892 in total

Arithmetic

Previous number37,488

Next number37,490

Double74,978

Half18,744.5

Square1,405,425,121

Cube52,687,982,361,169

Square root193.620763349≈irrational, shown to 9 decimal places

Cube root33.468374401≈

Negation-37,489

Reciprocal0.0000266745≈

Representations

Decimal37,489

Binary100100100111000116 bits

Octal111161

Hexadecimal9271

Base 36SXD

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

In wordsthirty-seven thousand, four hundred and eighty-nine

Ordinalthirty-seven thousand, four hundred and eighty-ninth

Scientific notation3.7489 × 10^4

Engineering notation37.489 × 10^3

In other bases

Ternary1220102111base 3; the most digit-efficient integer base after e: 10 digits

Quinary2144424base 5; one hand: 7 digits

Septenary214204base 7: 6 digits

Nonary56374base 9; each digit is two ternary digits: 5 digits

Duodecimal19841base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal4de9base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal10:24:49base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0T011T111digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11001011110110001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1001001001110001

Bit length16 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits9within that length

Bit parityodd7 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 15worth 32,768

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes292 71

Gray code1101101101001001n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1001001001110001

32-bit00000000000000001001001001110001

64-bit0000000000000000000000000000000000000000000000001001001001110001

One's complement0110110110001110at 16 bits, every bit flipped

Bits reversed1000111001001001at 16 bits

Rotated left by 10010010011100011at 16 bits, wrapping

Shifted left by 110010010011100010= 74,978, no wrap

Shifted right by 1100100100111000= 18,744, discarding the low bit

These bits as a double1.8522027 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime37,493+4

Previous prime37,483−6

Distance to nearest prime0, it is prime

Nearest square below37,249

Nearest square above37,636

Powers & multiples

37,489 to the power 21,405,425,121

37,489 to the power 352,687,982,361,169

37,489 to the power 41,975,219,770,737,864,641

37,489 to the power 574,049,013,985,191,807,526,449

First ten multiples37,489, 74,978, 112,467, 149,956, 187,445, 224,934, 262,423, 299,912, 337,401, 374,890

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 4

Divisible by 6No, remainder 1

Divisible by 7No, remainder 4

Divisible by 8No, remainder 1

Divisible by 9No, remainder 4

Divisible by 10No, remainder 9

Divisible by 11No, remainder 1

Divisible by 12No, remainder 1

Divisible by 100No, remainder 89

Collatz (3n + 1) trajectory

Steps to reach 162the total stopping time

Highest value reached112,4683× the starting value

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

First steps37,489 → 112,468 → 56,234 → 28,117 → 84,352 → 42,176 → 21,088 → 10,544 → 5,272 → 2,636 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,748,900%

37,489% as a decimal374.89

37,489% of 10037,489

37,489% of 1,000374,890

As a fraction of 10037,489/100

Read another way

As seconds10 hours, 24 minutes and 49 seconds

As bytes36.61 KiB

As a 24-bit colour#009271

Keep nerding

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