Recognised as Number

1,998,397

Positive
Odd
Prime
7 digits

1,998,397 is an odd 7-digit integer and a prime number. It has 2 divisors and a digital root of 1.

Number properties

ParityOddnot divisible by 2

SignPositive

PrimalityPrime

Absolute value1,998,397

Digit count7

Digit sum46

Digit product122,472

Multiplicative persistence4times the digit product can be taken before one digit is left

Digital root1repeated digit sum

PalindromicNoreads differently backwards

Happy numberNosquared-digit sums reach 1

Harshad numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation1,998,397

Distinct prime factors11,998,397

Number of divisors2

Sum of divisors σ(n)1,998,398

Aliquot sum1sum of the proper divisors

ClassificationDeficientthe aliquot sum is less than the number

Euler's totient φ(n)1,998,396integers below n that share no factor with it

Carmichael function λ(n)1,998,396the smallest exponent with aˣ ≡ 1 for every unit coprime to n

Möbius function μ(n)−11 distinct prime factor, an odd number of them

SquarefreeYesno repeated prime factor

All divisors1, 1,998,3972 in total

Arithmetic

Previous number1,998,396

Next number1,998,398

Double3,996,794

Half999,198.5

Square3,993,590,569,609

Cube7,980,779,413,534,916,773

Square root1,413.646702681≈irrational, shown to 9 decimal places

Cube root125.958435102≈

Negation-1,998,397

Reciprocal5.00401071 × 10^-7≈

Representations

Decimal1,998,397

Binary11110011111100011110121 bits

Octal7477075

Hexadecimal1E7E3D

Base 3616TZ1

Roman numeralNot defined above 3,999there is no agreed standard notation

In wordsone million, nine hundred and ninety-eight thousand, three hundred and ninety-seven

Ordinalone million, nine hundred and ninety-eight thousand, three hundred and ninety-seventh

Scientific notation1.998397 × 10^6

Engineering notation1.998397 × 10^6

In other bases

Ternary10202112021201base 3; the most digit-efficient integer base after e: 14 digits

Quinary1002422042base 5; one hand: 10 digits

Septenary22662142base 7: 8 digits

Nonary3675251base 9; each digit is two ternary digits: 7 digits

Duodecimal804591base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimalc9fjhbase 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal9:15:6:37base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary11T10TTT10TT01digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary11000111000001001001101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000111100111111000111101

Bit length21 bitsto write the magnitude

Set bits15the population count, or Hamming weight

Zero bits6within that length

Bit parityodd15 set bits, so odd; not the same as the number itself being odd

Highest set bitbit 20worth 1,048,576

Lowest set bitbit 00 trailing zeros

Power of twoNo

Bytes31e 7e 3d

Gray code100010100000100100011n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000111100111111000111101

64-bit0000000000000000000000000000000000000000000111100111111000111101

One's complement11111111111000011000000111000010at 32 bits, every bit flipped

Bits reversed10111100011111100111100000000000at 32 bits

Rotated left by 100000000001111001111110001111010at 32 bits, wrapping

Shifted left by 11111001111110001111010= 3,996,794, no wrap

Shifted right by 111110011111100011110= 999,198, discarding the low bit

These bits as a double9.87339304 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,998,413+16

Previous prime1,998,379−18

Distance to nearest prime0, it is prime

Nearest square below1,996,569

Nearest square above1,999,396

Powers & multiples

1,998,397 to the power 23,993,590,569,609

1,998,397 to the power 37,980,779,413,534,916,773

1,998,397 to the power 415,948,765,637,669,937,074,412,881

1,998,397 to the power 531,871,965,404,022,689,239,695,478,151,757

First ten multiples1,998,397, 3,996,794, 5,995,191, 7,993,588, 9,991,985, 11,990,382, 13,988,779, 15,987,176, 17,985,573, 19,983,970

Powers of twoBetween 2^20 (1,048,576) and 2^21 (2,097,152)

Divisibility tests

Divisible by 2No, remainder 1

Divisible by 3No, remainder 1

Divisible by 4No, remainder 1

Divisible by 5No, remainder 2

Divisible by 6No, remainder 1

Divisible by 7No, remainder 2

Divisible by 8No, remainder 5

Divisible by 9No, remainder 1

Divisible by 10No, remainder 7

Divisible by 11No, remainder 5

Divisible by 12No, remainder 1

Divisible by 100No, remainder 97

Collatz (3n + 1) trajectory

Steps to reach 1140the total stopping time

Highest value reached5,995,1923× the starting value

Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven

First steps1,998,397 → 5,995,192 → 2,997,596 → 1,498,798 → 749,399 → 2,248,198 → 1,124,099 → 3,372,298 → 1,686,149 → 5,058,448 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage199,839,700%

1,998,397% as a decimal19,983.97

1,998,397% of 1001,998,397

1,998,397% of 1,00019,983,970

As a fraction of 1001,998,397/100

Read another way

As seconds23 days, 3 hours and 6 minutes

As bytes1.906 MiB

As a 24-bit colour#1E7E3D

Keep nerding

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