Recognised as Number

40,201

Positive
Odd
Composite
5 digits

40,201 is an odd 5-digit integer and a composite number. It has 4 divisors and a digital root of 7.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityComposite

Absolute value40,201

Digit count5

Digit sum7

Digit product0zero, because one of the digits is zero

Multiplicative persistence1times the digit product can be taken before one digit is left

Digital root7repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation7 × 5,743

Distinct prime factors27, 5,743

Number of divisors4

Sum of divisors σ(n)45,952

Aliquot sum5,751sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)34,452integers below n that share no factor with it

Carmichael function λ(n)5,742the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 34,452

Möbius function μ(n)+12 distinct prime factors, an even number of them

SquarefreeYesno repeated prime factor

All divisors1, 7, 5,743, 40,2014 in total

Arithmetic

Previous number40,200

Next number40,202

Double80,402

Half20,100.5

Square1,616,120,401

Cube64,969,656,240,601

Square root200.501870315≈irrational, shown to 9 decimal places

Cube root34.256707444≈

Negation-40,201

Reciprocal0.000024875≈

Representations

Decimal40,201

Binary100111010000100116 bits

Octal116411

Hexadecimal9D09

Base 36V0P

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

In wordsforty thousand, two hundred and one

Ordinalforty thousand, two hundred and first

Scientific notation4.0201 × 10^4

Engineering notation40.201 × 10^3

In other bases

Ternary2001010221base 3; the most digit-efficient integer base after e: 10 digits

Quinary2241301base 5; one hand: 7 digits

Septenary225130base 7: 6 digits

Nonary61127base 9; each digit is two ternary digits: 5 digits

Duodecimal1b321base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal50a1base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:10:1base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0010110T1digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110110100011001base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1001110100001001

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

Bytes29d 09

Gray code1101001110001101n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1001110100001001

32-bit00000000000000001001110100001001

64-bit0000000000000000000000000000000000000000000000001001110100001001

One's complement0110001011110110at 16 bits, every bit flipped

Bits reversed1001000010111001at 16 bits

Rotated left by 10011101000010011at 16 bits, wrapping

Shifted left by 110011101000010010= 80,402, no wrap

Shifted right by 1100111010000100= 20,100, discarding the low bit

These bits as a double1.9861933 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime40,213+12

Previous prime40,193−8

Distance to nearest prime8

Nearest square below40,000

Nearest square above40,401

Powers & multiples

40,201 to the power 21,616,120,401

40,201 to the power 364,969,656,240,601

40,201 to the power 42,611,845,150,528,400,801

40,201 to the power 5104,998,786,896,392,240,601,001

First ten multiples40,201, 80,402, 120,603, 160,804, 201,005, 241,206, 281,407, 321,608, 361,809, 402,010

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 1

Divisible by 6No, remainder 1

Divisible by 7Yes

Divisible by 8No, remainder 1

Divisible by 9No, remainder 7

Divisible by 10No, remainder 1

Divisible by 11No, remainder 7

Divisible by 12No, remainder 1

Divisible by 100No, remainder 1

Collatz (3n + 1) trajectory

Steps to reach 193the total stopping time

Highest value reached203,5245× the starting value

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

First steps40,201 → 120,604 → 60,302 → 30,151 → 90,454 → 45,227 → 135,682 → 67,841 → 203,524 → 101,762 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,020,100%

40,201% as a decimal402.01

40,201% of 10040,201

40,201% of 1,000402,010

As a fraction of 10040,201/100

Read another way

As seconds11 hours, 10 minutes and 1 second

As bytes39.259 KiB

As a 24-bit colour#009D09

Keep nerding

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