Math question: If the number 6084 is expressed as the sum of two perfect cubes, what are the possible values of those two cubes?

To find the possible values of the two cubes, we can express 6084 as the sum of two cubes using the identity (a^3 + b^3) = (a + b)(a^2 - ab + b^2). So, we have 6084 = (a + b)(a^2 - ab + b^2). We need to find two positive integers a and b such that this equation holds. Since 6084 is even, one of the factors (a + b) must be even, and the other (a^2 - ab + b^2) must also be even. This means that both a and b must be either even or odd for the equation to be satisfied. By trying different values of a and b, we find that the possible values are: 1) a = 54, b = 54 2) a = 72, b = 36 3) a = 36, b = 72 4) a = 18, b = 72 5) a = 72, b = 18 6) a = 12, b = 72 7) a = 72, b = 12 8) a = 6, b = 72 9) a = 72, b = 6 10) a = 4, b = 72 11) a = 72, b = 4 12) a = 2, b = 72 13) a = 72, b = 2 These are the possible values of the two perfect cubes that sum up to 6084.

Max	9223372036854775807
25835	Positive integer
0b10001100	Binary number
01771452	Octal number
0x129abf	Hex number
5.012 * 10^7	Scientific notation
2^4 * 5	Factorized form
*	Random number

6084 (number)

6084 is an even 4-digits composite number following 6083 and preceding 6085. In scientific notation, it is written as 6.084 × 10^3. The sum of its digits is 18. It has a total of 6 prime factors and 27 positive divisors. There are 1872 positive integers (up to 6084) that are relatively prime to 6084.

Interesting facts

6084 has 27 divisors, whose sum is 16653
The reverse of 6084 is 4806
Previous prime number is 13

Basic properties

Is Prime? no
Number parity even
Number length 4
Sum of Digits 18
Digital Root 9

Name

Name	six thousand eighty-four

Notation

Scientific notation	6.084 × 10^3
Engineering notation	6.084 × 10^3

Prime Factorization of 6084

Prime Factorization 2 × 2 × 3 × 3 × 13 × 13

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	6	Total number of prime factors
rad	Radical	78	Product of the distinct prime numbers

The prime factorization of 6084 is 2 × 2 × 3 × 3 × 13 × 13. Since it has a total of 6 prime factors.

Most popular turbo-numbers

6, 9, 90, 89, 40, 377, 3142, 8639, 55272, 95129, 700318, 875647, 9022681, 3754822, 99707208, 4506826, 526036099, 965229641, 2722633637, 7358024824

Basic calculations (n = 6084)

Multiplication

n×y

n×2	12168
n×3	18252
n×4	24336
n×5	30420

Division

n÷y

n÷2	3042
n÷3	2028
n÷3	1521
n÷5	1216.8

Exponentiation

n^y

n²	37015056
n³	225199600704
n⁴	1370114370683136
n⁵	8335775831236199424

Nth Root

^y√n

²√n	78
³√n	18.255612210289
⁴√n	8.8317608663278
⁵√n	5.7126529511247

Divisors of 6084

1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 169, 234, 338, 468, 507, 676, 1014, 1521, 2028, 3042, 6084

27 divisors

τ	Total Divisors	27	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-6083	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.037037037037037	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	1	Returns the nth root of the product of n divisors
H	Harmonic Mean	27	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 6084 can be divided by 27 positive divisors. The sum of these divisors (counting 6084) is 1, the average is 0.037037037037037.

Base conversion 6084

Base	System	Value
2	Binary	1011111000100
3	Ternary	22100100
4	Quaternary	1133010
5	Quinary	143314
6	Senary	44100
8	Octal	13704
10	Decimal	6084
12	Duodecimal	3630
16	Hexadecimal	17c4
20	Vigesimal	f44
36	Base36	4p0

Cryptographic Hash Functions

md5	0d770c496aa3da6d2c3f2bd19e7b9d6b
sha1	ecc8960598eece6384e562b381c74adbdf84c291
sha256	afcbb3a0b0d252e8eb1f2ba0ccb8bac1e5a93befea32241badfbd759713f30fa
sha512	5aeb4c71da76745dee7d655b996d9d05129b401eb339e474fe713a143ca11245376d52f81b1a54cbddd2d2ea5aaee9114de12a69ec8894af4df026cc27bf4f16
ripemd-160	403a9fee16dcd981664b68cebe472f128f1e3ca0

6084 as geometric shapes

Circle

Radius = n

Diameter	12168
Circumference	38226.899408881
Area	116286228.00181

Sphere

Radius = n

Volume	943313881550.72
Surface area	465144912.00726
Circumference	38226.899408881

Square

Length = n

Perimeter	24336
Area	37015056
Diagonal	8604.0753134779

Cube

Length = n

Surface area	222090336
Volume	225199600704
Space diagonal	10537.797113249

Equilateral Triangle

Length = n

Perimeter	18252
Area	16027989.409252
Altitude	5268.8985566245

Triangular Pyramid

Length = n

Surface area	16027989.409252
Volume	26540027463.05
Height	2868.0251044926