Math Question: What is the largest prime factor of 1188?

To find the prime factors of 1188, we start by dividing it by the smallest prime number, 2. The result is 594. Dividing 594 by 2 again, we get 297. Continuing the process, dividing 297 by 3 gives us 99, and dividing 99 by 3 gives us 33. Continuing further, 33 can be divided by 3 to yield 11. Thus, the prime factorization of 1188 is 2^2 × 3^3 × 11. The largest prime factor here is 11. So, the answer is 11.

Question: What is the smallest positive integer divisible by 2, 3, 4, 6, 9, and 12, that is greater than or equal to 1188?

To find the smallest positive integer divisible by all the given factors, we can find their least common multiple (LCM). Prime factorizing each number, we have 2 = 2^1, 3 = 3^1, 4 = 2^2, 6 = 2^1 * 3^1, 9 = 3^2, and 12 = 2^2 * 3^1. The LCM is the highest power of each prime factor that appears in any of the numbers, which is obtained by taking the maximum exponent for each prime factor: 2^2 * 3^2 = 12 * 9 = 108. Since we are looking for a number greater than or equal to 1188, we need to find the smallest multiple of 108 that satisfies this condition. Dividing 1188 by 108, we get 11 with a remainder of 60. Since the remainder is non-zero, we need to add another 108 to obtain the next multiple. Thus, the smallest positive integer divisible by 2, 3, 4, 6, 9, and 12, that is greater than or equal to 1188 is 11 * 108 = 1188 + 108 = 1296.

Math question for the number 1188: What is the sum of all the positive divisors of 1188?

To find the sum of all the positive divisors of 1188, we need to list out its divisors. The prime factorization of 1188 is 2^2 * 3^4 * 11^1. Since the exponent of 2 is 2, we will have (2^0 + 2^1 + 2^2) as the divisors of 2. Similarly, for 3, we will have (3^0 + 3^1 + 3^2 + 3^3 + 3^4) and for 11, just (11^0 + 11^1). Calculating the sums, we get: (2^0 + 2^1 + 2^2) = 1 + 2 + 4 = 7 (3^0 + 3^1 + 3^2 + 3^3 + 3^4) = 1 + 3 + 9 + 27 + 81 = 121 (11^0 + 11^1) = 1 + 11 = 12 Finally, we calculate the product of these sums: 7 * 121 * 12 = 97944. Hence, the sum of all the positive divisors of 1188 is 97944.

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

1188 (number)

1188 is an even 4-digits composite number following 1187 and preceding 1189. In scientific notation, it is written as 1.188 × 10^3. The sum of its digits is 18. It has a total of 6 prime factors and 24 positive divisors. There are 360 positive integers (up to 1188) that are relatively prime to 1188.

Interesting facts

1188 has 24 divisors, whose sum is 3360
The reverse of 1188 is 8811
Previous prime number is 3

Basic properties

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

Name

Name	one thousand one hundred eighty-eight

Notation

Scientific notation	1.188 × 10^3
Engineering notation	1.188 × 10^3

Prime Factorization of 1188

Prime Factorization 2 × 2 × 11 × 3 × 3 × 3

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	6	Total number of prime factors
rad	Radical	66	Product of the distinct prime numbers

The prime factorization of 1188 is 2 × 2 × 11 × 3 × 3 × 3. Since it has a total of 6 prime factors.

Most popular turbo-numbers

3, 6, 20, 84, 623, 721, 6396, 5166, 77217, 12576, 73655, 13214, 1812816, 9847026, 66407923, 37964316, 377881423, 133291362, 8588080624, 9957181953

Basic calculations (n = 1188)

Multiplication

n×y

n×2	2376
n×3	3564
n×4	4752
n×5	5940

Division

n÷y

n÷2	594
n÷3	396
n÷3	297
n÷5	237.6

Exponentiation

n^y

n²	1411344
n³	1676676672
n⁴	1991891886336
n⁵	2366367560967168

Nth Root

^y√n

²√n	34.467375879228
³√n	10.591045005978
⁴√n	5.8708922558013
⁵√n	4.1206268505694

Divisors of 1188

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 99, 108, 132, 198, 297, 396, 594, 1188

24 divisors

τ	Total Divisors	24	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-1187	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.041666666666667	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	24	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1188 can be divided by 24 positive divisors. The sum of these divisors (counting 1188) is 1, the average is 0.041666666666667.

Base conversion 1188

Base	System	Value
2	Binary	10010100100
3	Ternary	1122000
4	Quaternary	102210
5	Quinary	14223
6	Senary	5300
8	Octal	2244
10	Decimal	1188
12	Duodecimal	830
16	Hexadecimal	4a4
20	Vigesimal	2j8
36	Base36	x0

Cryptographic Hash Functions

md5	c44e503833b64e9f27197a484f4257c0
sha1	de81d9d9c77a733524fab8bcc691f1ebd5a69f6e
sha256	b62764dc19af7e6a2fd312662a2fe207d273a883e64bf87bd0ec755007649e6c
sha512	81b2b56f34f7f0b3c1846acf414b26d3c0c217f404704de06a120e5d2a776457e97bda76dc9a7f5805b0adbc24fffc37696411bce6fe2fab07eb8e5b1b6149ad
ripemd-160	7d35323c9114f165a879cedd3ee905bbfe258820

1188 as geometric shapes

Circle

Radius = n

Diameter	2376
Circumference	7464.4241449293
Area	4433867.942088

Sphere

Radius = n

Volume	7023246820.2674
Surface area	17735471.768352
Circumference	7464.4241449293

Square

Length = n

Perimeter	4752
Area	1411344
Diagonal	1680.0857120992

Cube

Length = n

Surface area	8468064
Volume	1676676672
Space diagonal	2057.6763593918

Equilateral Triangle

Length = n

Perimeter	3564
Area	611129.87873937
Altitude	1028.8381796959

Triangular Pyramid

Length = n

Surface area	611129.87873937
Volume	197598240.77142
Height	560.02857069975