Math Question: What is the least common multiple (LCM) of 9984, 3, 8, and 7?

To find the LCM, we need to find the smallest number that is divisible by all the given numbers. Let's find the prime factorization of each number: 9984 = 2^8 * 3^2, 3 = 3^1, 8 = 2^3, and 7 = 7^1. Now, take the highest exponent for each prime factor: 2^8 * 3^2 * 7^1. Multiplying these factors, we get the LCM as 2^8 * 3^2 * 7 = 41472. Therefore, the LCM of 9984, 3, 8, and 7 is 41,472.

Math Question: What is the smallest prime number that can divide exactly into 9984?

The prime factorization of 9984 is 2^11 * 3^2. To find the smallest prime divisor, we start with 2 and check each number. 2 does divide exactly into 9984, so the answer is 2.

Math Question: What is the sum of the first 100 positive even integers greater than 9984?

To find the sum of the first 100 positive even integers greater than 9984, we know that the first even number greater than 9984 is 9986. The nth even number can be represented as 9984 + 2n, where n starts from 1. Therefore, the sum of the first 100 positive even integers greater than 9984 is calculated as 9986 + 9988 + 9990 + ... + 11982 + 11984. We can observe that the difference between consecutive terms is always 2, and the number of terms is 100. Using the formula for the sum of an arithmetic series, which is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term, we can find that the last term is 9984 + 2(100 - 1) = 11984. Substituting the values into the formula, we have Sn = (100/2)(9986 + 11984) = 50(21970) = 1098500. Therefore, the sum of the first 100 positive even integers greater than 9984 is 1,098,500.

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

9984 (number)

9984 is an even 4-digits composite number following 9983 and preceding 9985. In scientific notation, it is written as 9.984 × 10^3. The sum of its digits is 30. It has a total of 10 prime factors and 36 positive divisors. There are 3072 positive integers (up to 9984) that are relatively prime to 9984.

Interesting facts

9984 has 36 divisors, whose sum is 28616
The reverse of 9984 is 4899
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 4
Sum of Digits 30
Digital Root 3

Name

Name	nine thousand nine hundred eighty-four

Notation

Scientific notation	9.984 × 10^3
Engineering notation	9.984 × 10^3

Prime Factorization of 9984

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

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	10	Total number of prime factors
rad	Radical	78	Product of the distinct prime numbers

The prime factorization of 9984 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 13. Since it has a total of 10 prime factors.

Most popular turbo-numbers

9, 6, 23, 19, 545, 482, 9751, 3200, 92817, 51108, 869830, 449317, 2609529, 6245351, 42420069, 32640615, 215240729, 860548677, 6942685393, 9983661294

Basic calculations (n = 9984)

Multiplication

n×y

n×2	19968
n×3	29952
n×4	39936
n×5	49920

Division

n÷y

n÷2	4992
n÷3	3328
n÷3	2496
n÷5	1996.8

Exponentiation

n^y

n²	99680256
n³	995207675904
n⁴	9936153436225536
n⁵	9.9202555907276E+19

Nth Root

^y√n

²√n	99.919967974374
³√n	21.532850448349
⁴√n	9.9959975977575
⁵√n	6.3075530878571

Divisors of 9984

1, 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 32, 39, 48, 52, 64, 78, 96, 104, 128, 156, 192, 208, 256, 312, 384, 416, 624, 768, 832, 1248, 1664, 2496, 3328, 4992, 9984

36 divisors

τ	Total Divisors	36	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-9983	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.027777777777778	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	36	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 9984 can be divided by 36 positive divisors. The sum of these divisors (counting 9984) is 1, the average is 0.027777777777778.

Base conversion 9984

Base	System	Value
2	Binary	10011100000000
3	Ternary	111200210
4	Quaternary	2130000
5	Quinary	304414
6	Senary	114120
8	Octal	23400
10	Decimal	9984
12	Duodecimal	5940
16	Hexadecimal	2700
20	Vigesimal	14j4
36	Base36	7pc

Cryptographic Hash Functions

md5	81930c54e08b6d26d9638dd2e4656dc1
sha1	f06d8cd744b94c1e0f3efc97a6d96ed55a5f396d
sha256	a72ee2ce95a69a578e4cad1a7ccc7b289b3fbc90d5c1f51f3c8302191ddf2f03
sha512	51f6262e8b94c1a3f9d7a5c4dfb1e1e0460d0a9b51a261fbcd59da7903636c16f1294fab114e50320a947798eacd87ab81ad3794b48b2ea463d7796ebfede220
ripemd-160	3eea46fefd2665127ca23023abb1951557625576

9984 as geometric shapes

Circle

Radius = n

Diameter	19968
Circumference	62731.322106881
Area	313154759.95755

Sphere

Radius = n

Volume	4168716164554.9
Surface area	1252619039.8302
Circumference	62731.322106881

Square

Length = n

Perimeter	39936
Area	99680256
Diagonal	14119.508206733

Cube

Length = n

Surface area	598081536
Volume	995207675904
Space diagonal	17292.795262768

Equilateral Triangle

Length = n

Perimeter	29952
Area	43162816.975868
Altitude	8646.3976313838

Triangular Pyramid

Length = n

Surface area	43162816.975868
Volume	117286349386.77
Height	4706.5027355777