Recognised as Number
1,050,000
- Positive
- Even
- Composite
- 7 digits
1,050,000 is an even 7-digit integer and a composite number. It has 120 divisors and a digital root of 6.
Number properties
ParityEvendivisible by 2
SignPositive
PrimalityComposite
Absolute value1,050,000
Digit count7
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 factorisation2^4 × 3 × 5^5 × 7
Distinct prime factors42, 3, 5, 7
Number of divisors120
Sum of divisors σ(n)3,874,752
Aliquot sum2,824,752sum of the proper divisors
ClassificationAbundantthe aliquot sum exceeds the number
Euler's totient φ(n)240,000integers below n that share no factor with it
Carmichael function λ(n)7,500the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 240,000
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, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 125, 140, 150, 168, 175, 200, 210, 240, 250, 280, 300, 336, 350, 375, 400, 420, 500, 525, 560, 600, 625, 700, 750, 840, 875, 1,000, 1,050, 1,200, 1,250, 1,400, 1,500, 1,680, 1,750, 1,875, 2,000, 2,100, 2,500, 2,625, 2,800, 3,000, 3,125, 3,500, 3,750, 4,200, 4,375, 5,000, 5,250, 6,000, 6,250, 7,000, 7,500, 8,400, 8,750, 9,375, 10,000, 10,500, 12,500, 13,125, 14,000, 15,000, 17,500, 18,750, 21,000, 21,875, 25,000, 26,250, 30,000, 35,000, 37,500, 42,000, 43,750, 50,000, 52,500, 65,625, 70,000, 75,000, 87,500, 105,000, 131,250, 150,000, 175,000, 210,000, 262,500, 350,000, 525,000, 1,050,000120 in total
Arithmetic
Previous number1,049,999
Next number1,050,001
Double2,100,000
Half525,000
Square1,102,500,000,000
Cube1,157,625,000,000,000,000
Square root1,024.695076596≈irrational, shown to 9 decimal places
Cube root101.639635681≈
Negation-1,050,000
Reciprocal9.52380952 × 10^-7≈
Representations
Decimal1,050,000
Binary10000000001011001000021 bits
Octal4002620
Hexadecimal100590
Base 36MI6O
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordsone million, fifty thousand
Ordinalone million, fifty thousandth
Scientific notation1.05 × 10^6
Engineering notation1.05 × 10^6
In other bases
Ternary1222100022220base 3; the most digit-efficient integer base after e: 13 digits
Quinary232100000base 5; one hand: 9 digits
Septenary11632140base 7: 8 digits
Nonary1870286base 9; each digit is two ternary digits: 7 digits
Duodecimal427780base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits
Vigesimal6b500base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits
Sexagesimal4:51:40:0base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary1T00T1001000T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary100000001101010010000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000000100000000010110010000
Bit length21 bitsto write the magnitude
Set bits5the population count, or Hamming weight
Zero bits16within that length
Bit parityodd5 set bits, so odd; not the same as the number itself being even
Highest set bitbit 20worth 1,048,576
Lowest set bitbit 44 trailing zeros
Power of twoNo
Bytes310 05 90
Gray code110000000011101011000n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000000100000000010110010000
64-bit0000000000000000000000000000000000000000000100000000010110010000
One's complement11111111111011111111101001101111at 32 bits, every bit flipped
Bits reversed00001001101000000000100000000000at 32 bits
Rotated left by 100000000001000000000101100100000at 32 bits, wrapping
Shifted left by 11000000000101100100000= 2,100,000, no wrap
Shifted right by 110000000001011001000= 525,000, discarding the low bit
These bits as a double5.18768928 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
1,050,000 to the power 21,102,500,000,000
1,050,000 to the power 31,157,625,000,000,000,000
1,050,000 to the power 41,215,506,250,000,000,000,000,000
1,050,000 to the power 51,276,281,562,500,000,000,000,000,000,000
First ten multiples1,050,000, 2,100,000, 3,150,000, 4,200,000, 5,250,000, 6,300,000, 7,350,000, 8,400,000, 9,450,000, 10,500,000
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 9No, remainder 6
Divisible by 10Yes
Divisible by 11No, remainder 6
Divisible by 12Yes
Divisible by 100Yes
Collatz (3n + 1) trajectory
Steps to reach 190the total stopping time
Highest value reached1,050,000
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps1,050,000 → 525,000 → 262,500 → 131,250 → 65,625 → 196,876 → 98,438 → 49,219 → 147,658 → 73,829 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage105,000,000%
1,050,000% as a decimal10,500
1,050,000% of 1001,050,000
1,050,000% of 1,00010,500,000
As a fraction of 1001,050,000/100
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