Recognised as Number
1,077,120
- Positive
- Even
- Composite
- 7 digits
1,077,120 is an even 7-digit integer and a composite number. It has 192 divisors and a digital root of 9.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value1,077,120
Digit count7
Digit sum18
Digit product0zero, because one of the digits is zero
Multiplicative persistence1times the digit product can be taken before one digit is left
Digital root9repeated digit sum
PalindromicNoreads differently backwards
Happy numberNosquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^7 × 3^2 × 5 × 11 × 17
Distinct prime factors52, 3, 5, 11, 17
Number of divisors192
Sum of divisors σ(n)4,296,240
Aliquot sum3,219,120sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)245,760integers below n that share no factor with it
Carmichael function λ(n)480the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 245,760
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 17, 18, 20, 22, 24, 30, 32, 33, 34, 36, 40, 44, 45, 48, 51, 55, 60, 64, 66, 68, 72, 80, 85, 88, 90, 96, 99, 102, 110, 120, 128, 132, 136, 144, 153, 160, 165, 170, 176, 180, 187, 192, 198, 204, 220, 240, 255, 264, 272, 288, 306, 320, 330, 340, 352, 360, 374, 384, 396, 408, 440, 480, 495, 510, 528, 544, 561, 576, 612, 640, 660, 680, 704, 720, 748, 765, 792, 816, 880, 935, 960, 990, 1,020, 1,056, 1,088, 1,122, 1,152, 1,224, 1,320, 1,360, 1,408, 1,440, 1,496, 1,530, 1,584, 1,632, 1,683, 1,760, 1,870, 1,920, 1,980, 2,040, 2,112, 2,176, 2,244, 2,448, 2,640, 2,720, 2,805, 2,880, 2,992, 3,060, 3,168, 3,264, 3,366, 3,520, 3,740, 3,960, 4,080, 4,224, 4,488, 4,896, 5,280, 5,440, 5,610, 5,760, 5,984, 6,120, 6,336, 6,528, 6,732, 7,040, 7,480, 7,920, 8,160, 8,415, 8,976, 9,792, 10,560, 10,880, 11,220, 11,968, 12,240, 12,672, 13,464, 14,960, 15,840, 16,320, 16,830, 17,952, 19,584, 21,120, 22,440, 23,936, 24,480, 26,928, 29,920, 31,680, 32,640, 33,660, 35,904, 44,880, 48,960, 53,856, 59,840, 63,360, 67,320, 71,808, 89,760, 97,920, 107,712, 119,680, 134,640, 179,520, 215,424, 269,280, 359,040, 538,560, 1,077,120192 in total
Arithmetic
Previous number1,077,119
Next number1,077,121
Double2,154,240
Half538,560
Square1,160,187,494,400
Cube1,249,661,153,968,128,000
Square root1,037.843918901≈irrational, shown to 9 decimal places
Cube root102.507276898≈
Negation-1,077,120
Reciprocal9.28401664 × 10^-7≈
Representations
Decimal1,077,120
Binary10000011011111000000021 bits
Octal4067600
Hexadecimal106F80
Base 36N340
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsone million, seventy-seven thousand, one hundred and twenty
Ordinalone million, seventy-seven thousand, one hundred and twentieth
Scientific notation1.07712 × 10^6
Engineering notation1.07712 × 10^6
In other bases
Ternary2000201112100base 3; the most digit-efficient integer base after e: 13 digits
Quinary233431440base 5; one hand: 9 digits
Septenary12104202base 7: 8 digits
Nonary2021470base 9; each digit is two ternary digits: 7 digits
Duodecimal43b400base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits
Vigesimal6ecg0base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits
Sexagesimal4:59:12:0base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary1T001T1TTTT100digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary100011011000010000000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000000100000110111110000000
Bit length21 bitsto write the magnitude
Set bits8the population count, or Hamming weight
Zero bits13within that length
Bit parityeven8 set bits, so even; not the same as the number itself being even
Highest set bitbit 20worth 1,048,576
Lowest set bitbit 77 trailing zeros
Power of twoNo
Bytes310 6f 80
Gray code110000101100001000000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000000100000110111110000000
64-bit0000000000000000000000000000000000000000000100000110111110000000
One's complement11111111111011111001000001111111at 32 bits, every bit flipped
Bits reversed00000001111101100000100000000000at 32 bits
Rotated left by 100000000001000001101111100000000at 32 bits, wrapping
Shifted left by 11000001101111100000000= 2,154,240, no wrap
Shifted right by 110000011011111000000= 538,560, discarding the low bit
These bits as a double5.32167988 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
1,077,120 to the power 21,160,187,494,400
1,077,120 to the power 31,249,661,153,968,128,000
1,077,120 to the power 41,346,035,022,162,150,031,360,000
1,077,120 to the power 51,449,841,243,071,295,041,778,483,200,000
First ten multiples1,077,120, 2,154,240, 3,231,360, 4,308,480, 5,385,600, 6,462,720, 7,539,840, 8,616,960, 9,694,080, 10,771,200
Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)
Divisibility tests
Divisible by 2Yes
Divisible by 3Yes
Divisible by 4Yes
Divisible by 5Yes
Divisible by 6Yes
Divisible by 7No, remainder 2
Divisible by 8Yes
Divisible by 9Yes
Divisible by 10Yes
Divisible by 11Yes
Divisible by 12Yes
Divisible by 100No, remainder 20
Collatz (3n + 1) trajectory
Steps to reach 1116the total stopping time
Highest value reached1,077,120
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1,077,120 → 538,560 → 269,280 → 134,640 → 67,320 → 33,660 → 16,830 → 8,415 → 25,246 → 12,623 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage107,712,000%
1,077,120% as a decimal10,771.2
1,077,120% of 1001,077,120
1,077,120% of 1,00010,771,200
As a fraction of 1001,077,120/100
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