Recognised as Number

40,200

Positive
Even
Composite
5 digits

40,200 is an even 5-digit integer and a composite number. It has 48 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value40,200

Digit count5

Digit sum6

Digit product0zero, because one of the digits is zero

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

Digital root6repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberYesdivisible by its own digit sum

Factors & divisors

Prime factorisation2^3 × 3 × 5^2 × 67

Distinct prime factors42, 3, 5, 67

Number of divisors48

Sum of divisors σ(n)126,480

Aliquot sum86,280sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)10,560integers below n that share no factor with it

Carmichael function λ(n)660the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 10,560

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

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 67, 75, 100, 120, 134, 150, 200, 201, 268, 300, 335, 402, 536, 600, 670, 804, 1,005, 1,340, 1,608, 1,675, 2,010, 2,680, 3,350, 4,020, 5,025, 6,700, 8,040, 10,050, 13,400, 20,100, 40,20048 in total

Arithmetic

Previous number40,199

Next number40,201

Double80,400

Half20,100

Square1,616,040,000

Cube64,964,808,000,000

Square root200.499376558≈irrational, shown to 9 decimal places

Cube root34.256423396≈

Negation-40,200

Reciprocal0.0000248756≈

Representations

Decimal40,200

Binary100111010000100016 bits

Octal116410

Hexadecimal9D08

Base 36V0O

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

In wordsforty thousand, two hundred

Ordinalforty thousand, two hundredth

Scientific notation4.02 × 10^4

Engineering notation40.2 × 10^3

In other bases

Ternary2001010220base 3; the most digit-efficient integer base after e: 10 digits

Quinary2241300base 5; one hand: 7 digits

Septenary225126base 7: 6 digits

Nonary61126base 9; each digit is two ternary digits: 5 digits

Duodecimal1b320base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 5 digits

Vigesimal50a0base 20; hands and feet, and the Mayan and Yoruba systems: 4 digits

Sexagesimal11:10:0base 60; Babylonian, and still how an hour and a circle are divided: 3 digits

Balanced ternary1T0010110T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11110110100011000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

1001110100001000

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 33 trailing zeros

Power of twoNo

Bytes29d 08

Gray code1101001110001100n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

16-bit1001110100001000

32-bit00000000000000001001110100001000

64-bit0000000000000000000000000000000000000000000000001001110100001000

One's complement0110001011110111at 16 bits, every bit flipped

Bits reversed0001000010111001at 16 bits

Rotated left by 10011101000010001at 16 bits, wrapping

Shifted left by 110011101000010000= 80,400, no wrap

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

These bits as a double1.9861439 × 10^-319≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime40,213+13

Previous prime40,193−7

Distance to nearest prime7

Nearest square below40,000

Nearest square above40,401

Powers & multiples

40,200 to the power 21,616,040,000

40,200 to the power 364,964,808,000,000

40,200 to the power 42,611,585,281,600,000,000

40,200 to the power 5104,985,728,320,320,000,000,000

First ten multiples40,200, 80,400, 120,600, 160,800, 201,000, 241,200, 281,400, 321,600, 361,800, 402,000

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

Divisibility tests

Divisible by 2Yes

Divisible by 3Yes

Divisible by 4Yes

Divisible by 5Yes

Divisible by 6Yes

Divisible by 7No, remainder 6

Divisible by 8Yes

Divisible by 9No, remainder 6

Divisible by 10Yes

Divisible by 11No, remainder 6

Divisible by 12Yes

Divisible by 100Yes

Collatz (3n + 1) trajectory

Steps to reach 1119the total stopping time

Highest value reached40,200

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

First steps40,200 → 20,100 → 10,050 → 5,025 → 15,076 → 7,538 → 3,769 → 11,308 → 5,654 → 2,827 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage4,020,000%

40,200% as a decimal402

40,200% of 10040,200

40,200% of 1,000402,000

As a fraction of 10040,200/100

Read another way

As seconds11 hours and 10 minutes

As bytes39.258 KiB

As a 24-bit colour#009D08

Keep nerding

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