Recognised as Number
3,720,000
- Positive
- Even
- Composite
- 7 digits
3,720,000 is an even 7-digit integer and a composite number. It has 140 divisors and a digital root of 3.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value3,720,000
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 numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^6 × 3 × 5^4 × 31
Distinct prime factors42, 3, 5, 31
Number of divisors140
Sum of divisors σ(n)12,695,936
Aliquot sum8,975,936sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)960,000integers below n that share no factor with it
Carmichael function λ(n)6,000the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 960,000
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, 16, 20, 24, 25, 30, 31, 32, 40, 48, 50, 60, 62, 64, 75, 80, 93, 96, 100, 120, 124, 125, 150, 155, 160, 186, 192, 200, 240, 248, 250, 300, 310, 320, 372, 375, 400, 465, 480, 496, 500, 600, 620, 625, 744, 750, 775, 800, 930, 960, 992, 1,000, 1,200, 1,240, 1,250, 1,488, 1,500, 1,550, 1,600, 1,860, 1,875, 1,984, 2,000, 2,325, 2,400, 2,480, 2,500, 2,976, 3,000, 3,100, 3,720, 3,750, 3,875, 4,000, 4,650, 4,800, 4,960, 5,000, 5,952, 6,000, 6,200, 7,440, 7,500, 7,750, 8,000, 9,300, 9,920, 10,000, 11,625, 12,000, 12,400, 14,880, 15,000, 15,500, 18,600, 19,375, 20,000, 23,250, 24,000, 24,800, 29,760, 30,000, 31,000, 37,200, 38,750, 40,000, 46,500, 49,600, 58,125, 60,000, 62,000, 74,400, 77,500, 93,000, 116,250, 120,000, 124,000, 148,800, 155,000, 186,000, 232,500, 248,000, 310,000, 372,000, 465,000, 620,000, 744,000, 930,000, 1,240,000, 1,860,000, 3,720,000140 in total
Arithmetic
Previous number3,719,999
Next number3,720,001
Double7,440,000
Half1,860,000
Square13,838,400,000,000
Cube51,478,848,000,000,000,000
Square root1,928.730152199≈irrational, shown to 9 decimal places
Cube root154.9462179≈
Negation-3,720,000
Reciprocal2.68817204 × 10^-7≈
Representations
Decimal3,720,000
Binary111000110000110100000022 bits
Octal16141500
Hexadecimal38C340
Base 3627QDC
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsthree million, seven hundred and twenty thousand
Ordinalthree million, seven hundred and twenty thousandth
Scientific notation3.72 × 10^6
Engineering notation3.72 × 10^6
In other bases
Ternary20222222212210base 3; the most digit-efficient integer base after e: 14 digits
Quinary1423020000base 5; one hand: 10 digits
Septenary43422324base 7: 8 digits
Nonary6888783base 9; each digit is two ternary digits: 7 digits
Duodecimal12b4940base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 7 digits
Vigesimal135000base 20; hands and feet, and the Mayan and Yoruba systems: 6 digits
Sexagesimal17:13:20:0base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary1T10000000T0T10digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary10010011100011101000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000001110001100001101000000
Bit length22 bitsto write the magnitude
Set bits8the population count, or Hamming weight
Zero bits14within that length
Bit parityeven8 set bits, so even; not the same as the number itself being even
Highest set bitbit 21worth 2,097,152
Lowest set bitbit 66 trailing zeros
Power of twoNo
Bytes338 c3 40
Gray code1001001010001011100000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000001110001100001101000000
64-bit0000000000000000000000000000000000000000001110001100001101000000
One's complement11111111110001110011110010111111at 32 bits, every bit flipped
Bits reversed00000010110000110001110000000000at 32 bits
Rotated left by 100000000011100011000011010000000at 32 bits, wrapping
Shifted left by 111100011000011010000000= 7,440,000, no wrap
Shifted right by 1111000110000110100000= 1,860,000, discarding the low bit
These bits as a double1.8379242 × 10^-317≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
3,720,000 to the power 213,838,400,000,000
3,720,000 to the power 351,478,848,000,000,000,000
3,720,000 to the power 4191,501,314,560,000,000,000,000,000
3,720,000 to the power 5712,384,890,163,200,000,000,000,000,000,000
First ten multiples3,720,000, 7,440,000, 11,160,000, 14,880,000, 18,600,000, 22,320,000, 26,040,000, 29,760,000, 33,480,000, 37,200,000
Powers of twoBetween 2^21 (2,097,152) and 2^22 (4,194,304)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7No, remainder 4
Divisible by 8Yes
Divisible by 9No, remainder 3
Divisible by 10Yes
Divisible by 11No, remainder 9
Divisible by 12Yes
Divisible by 100Yes
Collatz (3n + 1) trajectory
Steps to reach 1172the total stopping time
Highest value reached3,720,000
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps3,720,000 → 1,860,000 → 930,000 → 465,000 → 232,500 → 116,250 → 58,125 → 174,376 → 87,188 → 43,594 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage372,000,000%
3,720,000% as a decimal37,200
3,720,000% of 1003,720,000
3,720,000% of 1,00037,200,000
As a fraction of 1003,720,000/100
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