Recognised as Number

35,801

Positive
Odd
Prime
5 digits

35,801 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 value35,801

Digit count5

Digit sum17

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times 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 factorisation35,801

Distinct prime factors135,801

Number of divisors2

Sum of divisors σ(n)35,802

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)35,800integers below n that share no factor with it

Carmichael function λ(n)35,800the 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, 35,8012 in total

Arithmetic

Previous number35,800

Next number35,802

Double71,602

Half17,900.5

Square1,281,711,601

Cube45,886,557,027,401

Square root189.211521848≈irrational, shown to 9 decimal places

Cube root32.958318971≈

Negation-35,801

Reciprocal0.0000279322≈

Representations

Decimal35,801

Binary100010111101100116 bits

Octal105731

Hexadecimal8BD9

Base 36RMH

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

In wordsthirty-five thousand, eight hundred and one

Ordinalthirty-five thousand, eight hundred and first

Scientific notation3.5801 × 10^4

Engineering notation35.801 × 10^3

In other bases

Ternary1211002222base 3; the most digit-efficient integer base after e: 10 digits

Quinary2121201base 5; one hand: 7 digits

Septenary206243base 7: 6 digits

Nonary54088base 9; each digit is two ternary digits: 5 digits

Duodecimal18875base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal49a1base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal9:56:41base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1TT1101000Tdigits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11001110000101001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1000101111011001

Bit length16 bitsto write the magnitude

Set bits9the population count, or Hamming weight

Zero bits7within that length

Bit parityodd9 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

Bytes28b d9

Gray code1100111000110101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1000101111011001

32-bit00000000000000001000101111011001

64-bit0000000000000000000000000000000000000000000000001000101111011001

One's complement0111010000100110at 16 bits, every bit flipped

Bits reversed1001101111010001at 16 bits

Rotated left by 10001011110110011at 16 bits, wrapping

Shifted left by 110001011110110010= 71,602, no wrap

Shifted right by 1100010111101100= 17,900, discarding the low bit

These bits as a double1.76880442 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime35,803+2

Previous prime35,797−4

Distance to nearest prime0, it is prime

Nearest square below35,721

Nearest square above36,100

Powers & multiples

35,801 to the power 21,281,711,601

35,801 to the power 345,886,557,027,401

35,801 to the power 41,642,784,628,137,983,201

35,801 to the power 558,813,332,471,967,936,579,001

First ten multiples35,801, 71,602, 107,403, 143,204, 179,005, 214,806, 250,607, 286,408, 322,209, 358,010

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 1

Divisible by 6No, remainder 5

Divisible by 7No, remainder 3

Divisible by 8No, remainder 1

Divisible by 9No, remainder 8

Divisible by 10No, remainder 1

Divisible by 11No, remainder 7

Divisible by 12No, remainder 5

Divisible by 100No, remainder 1

Collatz (3n + 1) trajectory

Steps to reach 149the total stopping time

Highest value reached120,8323× the starting value

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

First steps35,801 → 107,404 → 53,702 → 26,851 → 80,554 → 40,277 → 120,832 → 60,416 → 30,208 → 15,104 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage3,580,100%

35,801% as a decimal358.01

35,801% of 10035,801

35,801% of 1,000358,010

As a fraction of 10035,801/100

Read another way

As seconds9 hours, 56 minutes and 41 seconds

As bytes34.962 KiB

As a 24-bit colour#008BD9

Keep nerding

Every link below is a page Nerdulator can generate from what it already knows about this value.