Recognised as Number

1,317,984

Positive
Even
Composite
7 digits

1,317,984 is an even 7-digit integer and a composite number. It has 24 divisors and a digital root of 6.

Number properties

ParityEvendivisible by 2

SignPositive

PrimalityComposite

Absolute value1,317,984

Digit count7

Digit sum33

Digit product6,048

Multiplicative persistence2times 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 numberNodivisible by its own digit sum

Factors & divisors

Prime factorisation2^5 × 3 × 13,729

Distinct prime factors32, 3, 13,729

Number of divisors24

Sum of divisors σ(n)3,459,960

Aliquot sum2,141,976sum of the proper divisors

ClassificationAbundantthe aliquot sum exceeds the number

Euler's totient φ(n)439,296integers below n that share no factor with it

Carmichael function λ(n)13,728the smallest exponent with aˣ ≡ 1 for every unit; smaller than φ(n) = 439,296

Möbius function μ(n)0zero, because a prime divides n twice

SquarefreeNohas a repeated prime factor

All divisors1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 13,729, 27,458, 41,187, 54,916, 82,374, 109,832, 164,748, 219,664, 329,496, 439,328, 658,992, 1,317,98424 in total

Arithmetic

Previous number1,317,983

Next number1,317,985

Double2,635,968

Half658,992

Square1,737,081,824,256

Cube2,289,446,051,060,219,904

Square root1,148.034842677≈irrational, shown to 9 decimal places

Cube root109.640257291≈

Negation-1,317,984

Reciprocal7.58734552 × 10^-7≈

Representations

Decimal1,317,984

Binary10100000111000110000021 bits

Octal5016140

Hexadecimal141C60

Base 36S8YO

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

In wordsone million, three hundred and seventeen thousand, nine hundred and eighty-four

Ordinalone million, three hundred and seventeen thousand, nine hundred and eighty-fourth

Scientific notation1.317984 × 10^6

Engineering notation1.317984 × 10^6

In other bases

Ternary2110221221020base 3; the most digit-efficient integer base after e: 13 digits

Quinary314133414base 5; one hand: 9 digits

Septenary14126343base 7: 8 digits

Nonary2427836base 9; each digit is two ternary digits: 7 digits

Duodecimal536880base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 6 digits

Vigesimal84ej4base 20; hands and feet, and the Mayan and Yoruba systems: 5 digits

Sexagesimal6:6:6:24base 60; Babylonian, and still how an hour and a circle are divided: 4 digits

Balanced ternary1T11100T0T11T0digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed

Negabinary101000110110110100000base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign

Bit-level

00000000000101000001110001100000

Bit length21 bitsto write the magnitude

Set bits7the population count, or Hamming weight

Zero bits14within that length

Bit parityodd7 set bits, so odd; 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 1c 60

Gray code111100001001001010000n XOR (n >> 1); successive values differ in exactly one bit

At each machine width

32-bit00000000000101000001110001100000

64-bit0000000000000000000000000000000000000000000101000001110001100000

One's complement11111111111010111110001110011111at 32 bits, every bit flipped

Bits reversed00000110001110000010100000000000at 32 bits

Rotated left by 100000000001010000011100011000000at 32 bits, wrapping

Shifted left by 11010000011100011000000= 2,635,968, no wrap

Shifted right by 110100000111000110000= 658,992, discarding the low bit

These bits as a double6.51170616 × 10^-318≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)

Nearest landmarks

Next prime1,317,989+5

Previous prime1,317,971−13

Distance to nearest prime5

Nearest square below1,317,904

Nearest square above1,320,201

Powers & multiples

1,317,984 to the power 21,737,081,824,256

1,317,984 to the power 32,289,446,051,060,219,904

1,317,984 to the power 43,017,453,264,160,552,869,953,536

1,317,984 to the power 53,976,955,122,911,382,113,752,841,191,424

First ten multiples1,317,984, 2,635,968, 3,953,952, 5,271,936, 6,589,920, 7,907,904, 9,225,888, 10,543,872, 11,861,856, 13,179,840

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 5No, remainder 4

Divisible by 6Yes

Divisible by 7No, remainder 3

Divisible by 8Yes

Divisible by 9No, remainder 6

Divisible by 10No, remainder 4

Divisible by 11No, remainder 8

Divisible by 12Yes

Divisible by 100No, remainder 84

Collatz (3n + 1) trajectory

Steps to reach 136the total stopping time

Highest value reached1,317,984

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

First steps1,317,984 → 658,992 → 329,496 → 164,748 → 82,374 → 41,187 → 123,562 → 61,781 → 185,344 → 92,672 → …

Last steps… → 5 → 16 → 8 → 4 → 2 → 1

As a percentage & fraction

As a percentage131,798,400%

1,317,984% as a decimal13,179.84

1,317,984% of 1001,317,984

1,317,984% of 1,00013,179,840

As a fraction of 1001,317,984/100

Read another way

As seconds15 days, 6 hours and 6 minutes

As bytes1.257 MiB

As a 24-bit colour#141C60

Keep nerding

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