What is the least common multiple of 5760, 2, 3, and 5?

To find the least common multiple (LCM), we need to find a number that is divisible by all the given numbers without leaving a remainder. Start by prime factorizing 5760: 2^6 × 3^1 × 5^1. Now, look for the highest exponent of each prime factor including in the factorization -- for the prime factors 2, 3, and 5. The LCM is then 2^6 × 3^1 × 5^1 = 5760. Thus, the LCM of 5760, 2, 3, and 5 is 5760.

Math question: If you divide the number 5760 by its largest factor less than 100, and then subtract the square root of 5760, what is the result?

To find the largest factor less than 100, we divide 5760 by its prime factors: 2, 2, 2, 2, 2, 3, 3, 5. Starting from the largest prime factor, 5, we divide 5760 by 5 to get 1152. Continuing this process, the largest factor less than 100 is 72. Next, we calculate the square root of 5760, which equals approximately 75.89. Finally, we subtract the square root of 5760 from 72: 72 - 75.89 ≈ -3.89. Therefore, the result is approximately -3.89.

Math question: What is the arithmetic mean of the factors of 5760?

To find the arithmetic mean of the factors of 5760, we first determine all its factors. Factors are pairs of numbers that multiply to give 5760. The factors of 5760 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 256, 288, 320, 360, 384, 480, 512, 576, 640, 720, 768, 960, 1024, 1152, 1280, 1440, 1536, 1920, 2048, 2304, 2560, 2880, 3072, 3840, 4608, 5120, 5760, 6144, 7680, and 9216. Then, we calculate the sum of all the factors of 5760, which is 27860. To find the arithmetic mean, we divide the sum by the total number of factors, which is 64. Therefore, the arithmetic mean of the factors of 5760 is 435.3125.

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

5760 (number)

5760 is an even 4-digits composite number following 5759 and preceding 5761. In scientific notation, it is written as 5.760 × 10^3. The sum of its digits is 18. It has a total of 10 prime factors and 48 positive divisors. There are 1536 positive integers (up to 5760) that are relatively prime to 5760.

Interesting facts

5760 has 48 divisors, whose sum is 19890
The reverse of 5760 is 0675
Previous prime number is 5

Basic properties

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

Name

Name	five thousand seven hundred sixty

Notation

Scientific notation	5.760 × 10^3
Engineering notation	5.760 × 10^3

Prime Factorization of 5760

Prime Factorization 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 3

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	10	Total number of prime factors
rad	Radical	30	Product of the distinct prime numbers

The prime factorization of 5760 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 3. Since it has a total of 10 prime factors.

Most popular turbo-numbers

9, 6, 19, 45, 391, 292, 122, 7110, 60114, 4508, 749785, 231672, 2970596, 4069338, 18760558, 92583667, 331292370, 273193634, 9652529381, 6794796232

Basic calculations (n = 5760)

Multiplication

n×y

n×2	11520
n×3	17280
n×4	23040
n×5	28800

Division

n÷y

n÷2	2880
n÷3	1920
n÷3	1440
n÷5	1152

Exponentiation

n^y

n²	33177600
n³	191102976000
n⁴	1100753141760000
n⁵	6340338096537600000

Nth Root

^y√n

²√n	75.894663844041
³√n	17.925618986229
⁴√n	8.7117543493857
⁵√n	5.6504690009895

Divisors of 5760

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760

48 divisors

τ	Total Divisors	48	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-5759	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.020833333333333	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	48	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 5760 can be divided by 48 positive divisors. The sum of these divisors (counting 5760) is 1, the average is 0.020833333333333.

Base conversion 5760

Base	System	Value
2	Binary	1011010000000
3	Ternary	21220100
4	Quaternary	1122000
5	Quinary	141020
6	Senary	42400
8	Octal	13200
10	Decimal	5760
12	Duodecimal	3400
16	Hexadecimal	1680
20	Vigesimal	e80
36	Base36	4g0

Cryptographic Hash Functions

md5	9ec51f6eb240fb631a35864e13737bca
sha1	6e9cb630b0be9e626dd4dfb69040fc982782274d
sha256	84b504f830bf8b6d2c233eead51d27a08d46a33ddf8225d90197e3f565f5d621
sha512	7286047889676e52b18e89d35a018c3b458bf937fc8c67794231fd23ef1b67d9c1271d51ab8546c60922b27de9a5a132252121a94626e75a7859c5571b16a1a5
ripemd-160	fad6a5334487c994bba6a1d31757ae3c711e606e

5760 as geometric shapes

Circle

Radius = n

Diameter	11520
Circumference	36191.147369354
Area	104230504.42374

Sphere

Radius = n

Volume	800490273974.33
Surface area	416922017.69496
Circumference	36191.147369354

Square

Length = n

Perimeter	23040
Area	33177600
Diagonal	8145.870119269

Cube

Length = n

Surface area	199065600
Volume	191102976000
Space diagonal	9976.6126515967

Equilateral Triangle

Length = n

Perimeter	17280
Area	14366322.218299
Altitude	4988.3063257984

Triangular Pyramid

Length = n

Surface area	14366322.218299
Volume	22521701705.755
Height	2715.2900397563