Recognised as Number
4,042,002
- Positive
- Even
- Composite
- 7 digits
4,042,002 is an even 7-digit integer and a composite number. It has 8 divisors and a digital root of 3.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value4,042,002
Digit count7
Digit sum12
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root3repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberNodivisible by its own digit sum
Factors & divisors
Prime factorisation2 × 3 × 673,667
Distinct prime factors32, 3, 673,667
Number of divisors8
Sum of divisors σ(n)8,084,016
Aliquot sum4,042,014sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)1,347,332integers below n that share no factor with it
Carmichael function λ(n)673,666the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 1,347,332
Möbius function μ(n)−13 distinct prime factors, an odd number of them
SquarefreeYesno repeated prime factor
All divisors1, 2, 3, 6, 673,667, 1,347,334, 2,021,001, 4,042,0028 in total
Arithmetic
Previous number4,042,001
Next number4,042,003
Double8,084,004
Half2,021,001
Square16,337,780,168,004
Cube66,037,340,114,632,504,008
Square root2,010.473078656≈irrational, shown to 9 decimal places
Cube root159.293788536≈
Negation-4,042,002
Reciprocal2.47402154 × 10^-7≈
Representations
Decimal4,042,002
Binary111101101011010001001022 bits
Octal17326422
Hexadecimal3DAD12
Base 362EMTU
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsfour million, forty-two thousand and two
Ordinalfour million, forty-two thousand and second
Scientific notation4.042002 × 10^6
Engineering notation4.042002 × 10^6
In other bases
Ternary21121100120210base 3; the most digit-efficient integer base after e: 14 digits
Quinary2013321002base 5; one hand: 10 digits
Septenary46233156base 7: 8 digits
Nonary7540523base 9; each digit is two ternary digits: 7 digits
Duodecimal142b156base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 7 digits
Vigesimal155502base 20; hands and feet, and the Mayan and Yoruba systems: 6 digits
Sexagesimal18:42:46:42base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary10TTT1101TT1T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary10000101111110100010110base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000001111011010110100010010
Bit length22 bitsto write the magnitude
Set bits12the population count, or Hamming weight
Zero bits10within that length
Bit parityeven12 set bits, so even; not the same as the number itself being even
Highest set bitbit 21worth 2,097,152
Lowest set bitbit 11 trailing zero
Power of twoNo
Bytes33d ad 12
Gray code1000110111101110011011n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000001111011010110100010010
64-bit0000000000000000000000000000000000000000001111011010110100010010
One's complement11111111110000100101001011101101at 32 bits, every bit flipped
Bits reversed01001000101101011011110000000000at 32 bits
Rotated left by 100000000011110110101101000100100at 32 bits, wrapping
Shifted left by 111110110101101000100100= 8,084,004, no wrap
Shifted right by 1111101101011010001001= 2,021,001, discarding the low bit
These bits as a double1.99701433 × 10^-317≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
4,042,002 to the power 216,337,780,168,004
4,042,002 to the power 366,037,340,114,632,504,008
4,042,002 to the power 4266,923,060,818,024,810,465,344,016
4,042,002 to the power 51,078,903,545,672,577,919,950,541,443,360,032
First ten multiples4,042,002, 8,084,004, 12,126,006, 16,168,008, 20,210,010, 24,252,012, 28,294,014, 32,336,016, 36,378,018, 40,420,020
Powers of twoBetween 2^21 (2,097,152) and 2^22 (4,194,304)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4No, remainder 2
Divisible by 5No, remainder 2
Divisible by 6Yes
Divisible by 7No, remainder 6
Divisible by 8No, remainder 2
Divisible by 9No, remainder 3
Divisible by 10No, remainder 2
Divisible by 11No, remainder 8
Divisible by 12No, remainder 6
Divisible by 100No, remainder 2
Collatz (3n + 1) trajectory
Steps to reach 1123the total stopping time
Highest value reached17,265,3644× the starting value
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps4,042,002 → 2,021,001 → 6,063,004 → 3,031,502 → 1,515,751 → 4,547,254 → 2,273,627 → 6,820,882 → 3,410,441 → 10,231,324 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage404,200,200%
4,042,002% as a decimal40,420.02
4,042,002% of 1004,042,002
4,042,002% of 1,00040,420,020
As a fraction of 1004,042,002/100
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