Recognised as Number

37,493

Positive
Odd
Prime
5 digits

37,493 is an odd 5-digit integer and a prime number. It has 2 divisors and a digital root of 8.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value37,493

Digit count5

Digit sum26

Digit product2,268

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root8repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation37,493

Distinct prime factors137,493

Number of divisors2

Sum of divisors σ(n)37,494

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)37,492integers below n that share no factor with it

Carmichael function λ(n)37,492the 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, 37,4932 in total

Arithmetic

Previous number37,492

Next number37,494

Double74,986

Half18,746.5

Square1,405,725,049

Cube52,704,849,262,157

Square root193.631092545≈irrational, shown to 9 decimal places

Cube root33.469564694≈

Negation-37,493

Reciprocal0.0000266716≈

Representations

Decimal37,493

Binary100100100111010116 bits

Octal111165

Hexadecimal9275

Base 36SXH

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

In wordsthirty-seven thousand, four hundred and ninety-three

Ordinalthirty-seven thousand, four hundred and ninety-third

Scientific notation3.7493 × 10^4

Engineering notation37.493 × 10^3

In other bases

Ternary1220102122base 3; the most digit-efficient integer base after e: 10 digits

Quinary2144433base 5; one hand: 7 digits

Septenary214211base 7: 6 digits

Nonary56378base 9; each digit is two ternary digits: 5 digits

Duodecimal19845base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal4dedbase 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal10:24:53base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0T0110T0Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11001011110110101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1001001001110101

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

Bytes292 75

Gray code1101101101001111n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1001001001110101

32-bit00000000000000001001001001110101

64-bit0000000000000000000000000000000000000000000000001001001001110101

One's complement0110110110001010at 16 bits, every bit flipped

Bits reversed1010111001001001at 16 bits

Rotated left by 10010010011101011at 16 bits, wrapping

Shifted left by 110010010011101010= 74,986, no wrap

Shifted right by 1100100100111010= 18,746, discarding the low bit

These bits as a double1.85240033 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime37,501+8

Previous prime37,489−4

Distance to nearest prime0, it is prime

Nearest square below37,249

Nearest square above37,636

Powers & multiples

37,493 to the power 21,405,725,049

37,493 to the power 352,704,849,262,157

37,493 to the power 41,976,062,913,386,052,401

37,493 to the power 574,088,526,811,583,262,670,693

First ten multiples37,493, 74,986, 112,479, 149,972, 187,465, 224,958, 262,451, 299,944, 337,437, 374,930

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

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 2

Divisible by 4No, remainder 1

Divisible by 5No, remainder 3

Divisible by 6No, remainder 5

Divisible by 7No, remainder 1

Divisible by 8No, remainder 5

Divisible by 9No, remainder 8

Divisible by 10No, remainder 3

Divisible by 11No, remainder 5

Divisible by 12No, remainder 5

Divisible by 100No, remainder 93

Collatz (3n + 1) trajectory

Steps to reach 1155the total stopping time

Highest value reached112,4803× the starting value

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

First steps37,493 → 112,480 → 56,240 → 28,120 → 14,060 → 7,030 → 3,515 → 10,546 → 5,273 → 15,820 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,749,300%

37,493% as a decimal374.93

37,493% of 10037,493

37,493% of 1,000374,930

As a fraction of 10037,493/100

Read another way

As seconds10 hours, 24 minutes and 53 seconds

As bytes36.614 KiB

As a 24-bit colour#009275

Keep nerding

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