Recognised as Number
6,998,221
- Positive
- Odd
- Prime
- 7 digits
6,998,221 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 value6,998,221
Digit count7
Digit sum37
Digit product15,552
Multiplicative persistence3times 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 factorisation6,998,221
Distinct prime factors16,998,221
Number of divisors2
Sum of divisors σ(n)6,998,222
Aliquot sum1sum of the proper divisors
ClassificationDeficientthe aliquot sum is less than the number
Euler's totient φ(n)6,998,220integers below n that share no factor with it
Carmichael function λ(n)6,998,220the 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, 6,998,2212 in total
Arithmetic
Previous number6,998,220
Next number6,998,222
Double13,996,442
Half3,499,110.5
Square48,975,097,164,841
Cube342,738,553,456,030,747,861
Square root2,645.415090302≈irrational, shown to 9 decimal places
Cube root191.276911644≈
Negation-6,998,221
Reciprocal1.42893458 × 10^-7≈
Representations
Decimal6,998,221
Binary1101010110010001100110123 bits
Octal32544315
Hexadecimal6AC8CD
Base 3645ZV1
Roman numeralNot defined above 3,999there is no agreed standard notation
In wordssix million, nine hundred and ninety-eight thousand, two hundred and twenty-one
Ordinalsix million, nine hundred and ninety-eight thousand, two hundred and twenty-first
Scientific notation6.998221 × 10^6
Engineering notation6.998221 × 10^6
In other bases
Ternary111011112202101base 3; the most digit-efficient integer base after e: 15 digits
Quinary3242420341base 5; one hand: 10 digits
Septenary113324656base 7: 9 digits
Nonary14145671base 9; each digit is two ternary digits: 8 digits
Duodecimal2415a91base 12; divides by 2, 3, 4 and 6, which is why eggs and inches come in twelves: 7 digits
Vigesimal23efb1base 20; hands and feet, and the Mayan and Yoruba systems: 6 digits
Sexagesimal32:23:57:1base 60; Babylonian, and still how an hour and a circle are divided: 4 digits
Balanced ternary1111TTTT0T1T101digits −1, 0 and +1 written T, 0 and 1; negation is swapping T and 1, so no sign is needed
Negabinary1101111111101100111011101base −2; place values alternate 1, −2, 4, −8, so every integer has exactly one form without a sign
Bit-level
00000000011010101100100011001101
Bit length23 bitsto write the magnitude
Set bits12the population count, or Hamming weight
Zero bits11within that length
Bit parityeven12 set bits, so even; not the same as the number itself being odd
Highest set bitbit 22worth 4,194,304
Lowest set bitbit 00 trailing zeros
Power of twoNo
Bytes36a c8 cd
Gray code10111111010110010101011n XOR (n >> 1); successive values differ in exactly one bit
At each machine width
32-bit00000000011010101100100011001101
64-bit0000000000000000000000000000000000000000011010101100100011001101
One's complement11111111100101010011011100110010at 32 bits, every bit flipped
Bits reversed10110011000100110101011000000000at 32 bits
Rotated left by 100000000110101011001000110011010at 32 bits, wrapping
Shifted left by 1110101011001000110011010= 13,996,442, no wrap
Shifted right by 11101010110010001100110= 3,499,110, discarding the low bit
These bits as a double3.45758058 × 10^-317≈IEEE-754 binary64 reinterpretation of the same 64 bits (subnormal)
Nearest landmarks
Powers & multiples
6,998,221 to the power 248,975,097,164,841
6,998,221 to the power 3342,738,553,456,030,747,861
6,998,221 to the power 42,398,560,142,305,616,956,326,555,281
6,998,221 to the power 516,785,653,957,646,157,001,720,582,025,155,101
First ten multiples6,998,221, 13,996,442, 20,994,663, 27,992,884, 34,991,105, 41,989,326, 48,987,547, 55,985,768, 62,983,989, 69,982,210
Powers of twoBetween 2^22 (4,194,304) and 2^23 (8,388,608)
Divisibility tests
Divisible by 2No, remainder 1
Divisible by 3No, remainder 1
Divisible by 4No, remainder 1
Divisible by 5No, remainder 1
Divisible by 6No, remainder 1
Divisible by 7No, remainder 6
Divisible by 8No, remainder 5
Divisible by 9No, remainder 1
Divisible by 10No, remainder 1
Divisible by 11No, remainder 10
Divisible by 12No, remainder 1
Divisible by 100No, remainder 21
Collatz (3n + 1) trajectory
Steps to reach 1191the total stopping time
Highest value reached20,994,6643× the starting value
Reaches 1Yesthe Collatz conjecture says every positive integer does, but it is unproven
First steps6,998,221 → 20,994,664 → 10,497,332 → 5,248,666 → 2,624,333 → 7,873,000 → 3,936,500 → 1,968,250 → 984,125 → 2,952,376 → …
Last steps… → 5 → 16 → 8 → 4 → 2 → 1
As a percentage & fraction
As a percentage699,822,100%
6,998,221% as a decimal69,982.21
6,998,221% of 1006,998,221
6,998,221% of 1,00069,982,210
As a fraction of 1006,998,221/100
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