Recognised as Number
1,320,480
- Positive
- Even
- Composite
- 7 digits
1,320,480 is an even 7-digit integer and a composite number. It has 144 divisors and a digital root of 9.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value1,320,480
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 numberYessquared-digit sums reach 1
Harshad numberYesdivisible by its own digit sum
Factors & divisors
Prime factorisation2^5 × 3^2 × 5 × 7 × 131
Distinct prime factors52, 3, 5, 7, 131
Number of divisors144
Sum of divisors σ(n)5,189,184
Aliquot sum3,868,704sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)299,520integers below n that share no factor with it
Carmichael function λ(n)1,560the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 299,520
Möbius function μ(n)0zero, because a prime divides n twice
SquarefreeNohas a repeated prime factor
All divisors1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 35, 36, 40, 42, 45, 48, 56, 60, 63, 70, 72, 80, 84, 90, 96, 105, 112, 120, 126, 131, 140, 144, 160, 168, 180, 210, 224, 240, 252, 262, 280, 288, 315, 336, 360, 393, 420, 480, 504, 524, 560, 630, 655, 672, 720, 786, 840, 917, 1,008, 1,048, 1,120, 1,179, 1,260, 1,310, 1,440, 1,572, 1,680, 1,834, 1,965, 2,016, 2,096, 2,358, 2,520, 2,620, 2,751, 3,144, 3,360, 3,668, 3,930, 4,192, 4,585, 4,716, 5,040, 5,240, 5,502, 5,895, 6,288, 7,336, 7,860, 8,253, 9,170, 9,432, 10,080, 10,480, 11,004, 11,790, 12,576, 13,755, 14,672, 15,720, 16,506, 18,340, 18,864, 20,960, 22,008, 23,580, 27,510, 29,344, 31,440, 33,012, 36,680, 37,728, 41,265, 44,016, 47,160, 55,020, 62,880, 66,024, 73,360, 82,530, 88,032, 94,320, 110,040, 132,048, 146,720, 165,060, 188,640, 220,080, 264,096, 330,120, 440,160, 660,240, 1,320,480144 in total
Arithmetic
Previous number1,320,479
Next number1,320,481
Double2,640,960
Half660,240
Square1,743,667,430,400
Cube2,302,477,968,494,592,000
Square root1,149.121403508≈irrational, shown to 9 decimal places
Cube root109.709425938≈
Negation-1,320,480
Reciprocal7.57300376 × 10^-7≈
Representations
Decimal1,320,480
Binary10100001001100010000021 bits
Octal5023040
Hexadecimal142620
Base 36SAW0
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsone million, three hundred and twenty thousand, four hundred and eighty
Ordinalone million, three hundred and twenty thousand, four hundred and eightieth
Scientific notation1.32048 × 10^6
Engineering notation1.32048 × 10^6
In other bases
Ternary2111002100200base 3; the most digit-efficient integer base after e: 13 digits
Quinary314223410base 5; one hand: 9 digits
Septenary14136540base 7: 8 digits
Nonary2432320base 9; each digit is two ternary digits: 7 digits
Duodecimal538200base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits
Vigesimal85140base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits
Sexagesimal6:6:48:0base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary1T11101T101T00digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary101000111101001100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000000101000010011000100000
Bit length21 bitsto write the magnitude
Set bits6the population count, or Hamming weight
Zero bits15within that length
Bit parityeven6 set bits, so even; not the same as the number itself being even
Highest set bitbit 20worth 1,048,576
Lowest set bitbit 55 trailing zeros
Power of twoNo
Bytes314 26 20
Gray code111100011010100110000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000000101000010011000100000
64-bit0000000000000000000000000000000000000000000101000010011000100000
One's complement11111111111010111101100111011111at 32 bits, every bit flipped
Bits reversed00000100011001000010100000000000at 32 bits
Rotated left by 100000000001010000100110001000000at 32 bits, wrapping
Shifted left by 11010000100110001000000= 2,640,960, no wrap
Shifted right by 110100001001100010000= 660,240, discarding the low bit
These bits as a double6.52403804 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
1,320,480 to the power 21,743,667,430,400
1,320,480 to the power 32,302,477,968,494,592,000
1,320,480 to the power 43,040,376,107,837,738,844,160,000
1,320,480 to the power 54,014,755,842,877,577,388,936,396,800,000
First ten multiples1,320,480, 2,640,960, 3,961,440, 5,281,920, 6,602,400, 7,922,880, 9,243,360, 10,563,840, 11,884,320, 13,204,800
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 7Yes
Divisible by 8Yes
Divisible by 9Yes
Divisible by 10Yes
Divisible by 11No, remainder 7
Divisible by 12Yes
Divisible by 100No, remainder 80
Collatz (3n + 1) trajectory
Steps to reach 1186the total stopping time
Highest value reached1,320,480
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1,320,480 → 660,240 → 330,120 → 165,060 → 82,530 → 41,265 → 123,796 → 61,898 → 30,949 → 92,848 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage132,048,000%
1,320,480% as a decimal13,204.8
1,320,480% of 1001,320,480
1,320,480% of 1,00013,204,800
As a fraction of 1001,320,480/100
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