Math question: What is the sum of all the positive divisors of 4140?

To find the sum of divisors, we factorize the number. The prime factorization of 4140 is 2^2 * 3 * 5 * 69. Now, to calculate the sum of divisors, we use the formula: (p₁^0 + p₁^1 + ... + p₁^n) * (p₂^0 + p₂^1 + ... + p₂^m) * ... * (pₖ^0 + pₖ^1 + ... + pₖ^q). Substituting the exponents, we have (2^0 + 2^1 + 2^2) * (3^0 + 3^1) * (5^0 + 5^1) * (69^0 + 69^1). Simplifying, we get (1 + 2 + 4) * (1 + 3) * (1 + 5) * (1 + 69). This results in 7 * 4 * 6 * 70, which equals 117,600. The sum of all positive divisors of 4140 is 117,600.

Math Question: Determine the sum of the divisors of the number 4140.

To find the sum of the divisors of 4140, we begin by finding the prime factorization of 4140 which is 2^2 × 3 × 5 × 7 × 11. Now, we can apply the sum-of-divisors formula: The sum of divisors = (2^0 + 2^1 + 2^2) × (3^0 + 3^1) × (5^0 + 5^1) × (7^0 + 7^1) × (11^0 + 11^1) Considering all possible combinations, the sum comes out to be (1 + 2 + 4) × (1 + 3) × (1 + 5) × (1 + 7) × (1 + 11) = 15 × 4 × 6 × 8 × 12 = 691,200. Therefore, the sum of the divisors of 4140 is 691,200.

Math Question: Find the largest prime factor of the number 4140.

To determine the largest prime factor of 4140, first, factorize it as 2^3 x 3 x 5 x 23. Thus, the prime factorization of 4140 is 2^3 x 3 x 5 x 23. The largest prime factor is 23.

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

4140 (number)

4140 is an even 4-digits composite number following 4139 and preceding 4141. In scientific notation, it is written as 4.140 × 10^3. The sum of its digits is 9. It has a total of 5 prime factors and 24 positive divisors. There are 1056 positive integers (up to 4140) that are relatively prime to 4140.

Interesting facts

4140 has 24 divisors, whose sum is 10080
The reverse of 4140 is 0414
Previous prime number is 5

Basic properties

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

Name

Name	four thousand one hundred forty

Notation

Scientific notation	4.140 × 10^3
Engineering notation	4.140 × 10^3

Prime Factorization of 4140

Prime Factorization 2 × 2 × 9 × 5 × 23

Composite number

ω	Distinct Factors	4	Total number of distinct prime factors
Ω	Total Factors	5	Total number of prime factors
rad	Radical	2070	Product of the distinct prime numbers

The prime factorization of 4140 is 2 × 2 × 9 × 5 × 23. Since it has a total of 5 prime factors.

Most popular turbo-numbers

8, 10, 59, 16, 974, 752, 3206, 4402, 2110, 78343, 449414, 16812, 8977977, 4751135, 37642603, 86638975, 318374463, 8843869, 6479875115, 8803689015

Basic calculations (n = 4140)

Multiplication

n×y

n×2	8280
n×3	12420
n×4	16560
n×5	20700

Division

n÷y

n÷2	2070
n÷3	1380
n÷3	1035
n÷5	828

Exponentiation

n^y

n²	17139600
n³	70957944000
n⁴	293765888160000
n⁵	1216190776982400000

Nth Root

^y√n

²√n	64.342831768582
³√n	16.057087736312
⁴√n	8.0213983674034
⁵√n	5.2893227513973

Divisors of 4140

1, 2, 4, 5, 9, 10, 18, 20, 23, 36, 45, 46, 90, 92, 115, 180, 207, 230, 414, 460, 828, 1035, 2070, 4140

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	-4139	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 4140 can be divided by 24 positive divisors. The sum of these divisors (counting 4140) is 1, the average is 0.041666666666667.

Base conversion 4140

Base	System	Value
2	Binary	1000000101100
3	Ternary	12200100
4	Quaternary	1000230
5	Quinary	113030
6	Senary	31100
8	Octal	10054
10	Decimal	4140
12	Duodecimal	2490
16	Hexadecimal	102c
20	Vigesimal	a70
36	Base36	370

Cryptographic Hash Functions

md5	4f05d4821fe9967817dea5a20c4e7b35
sha1	89446530a6a5fd76d714c1c6ca536a3241040d5f
sha256	1f74494f923e9bf4bedc9968f0418824c2b298bd83009812a45e547f6733ac7b
sha512	fb347ff6f4bcf847487b074495d327ae941cf58d4c71e31745300c59fed205e75dd63f172f44bcc54cfe7d89412a780b550dcd73fa7ee3c534db55db173b52a1
ripemd-160	81c02032f92f7641ece33e99831c7b770e032cc3

4140 as geometric shapes

Circle

Radius = n

Diameter	8280
Circumference	26012.387171723
Area	53845641.445468

Sphere

Radius = n

Volume	297227940778.98
Surface area	215382565.78187
Circumference	26012.387171723

Square

Length = n

Perimeter	16560
Area	17139600
Diagonal	5854.8441482246

Cube

Length = n

Surface area	102837600
Volume	70957944000
Space diagonal	7170.6903433352

Equilateral Triangle

Length = n

Perimeter	12420
Area	7421664.5053519
Altitude	3585.3451716676

Triangular Pyramid

Length = n

Surface area	7421664.5053519
Volume	8362473896.9092
Height	1951.6147160749