Question: Consider a four-digit number where the digits are arranged in ascending and descending order. Repeat the process of rearranging the digits in ascending and descending order. Find the number of iterations required to reach the constant number 6174 as the rearranged number.

To solve, let's choose an example: Starting with 4321, rearranging the digits gives 1234. Performing this procedure again gives 4321 - 1234 = 3087. Repeating one more time yields 8730 - 0378 = 8352. Iterating once more: 8532 - 2358 = 6174. Therefore, it takes four iterations for the number to reach 6174. This pattern is consistent for all different four-digit numbers (except those consisting of a single digit repeated).

Math question: How many iterations are needed for the number 6174 to reach its fixed point using the Kaprekar's Routine?

To understand the answer, we need to delve into the Kaprekar's Routine based on the number 6174. 1. Choose any 4-digit number (greater than 0) that contains at least two distinct digits. 2. Rearrange the digits to form the largest and smallest possible numbers. 3. Subtract the smallest number from the largest number. 4. Repeat steps 2 and 3 until reaching the fixed point number 6174. For example, starting with the number 6174: - 7641 - 1467 = 6174 Regardless of the initial number chosen, it takes exactly one iteration to reach 6174 as it is considered the fixed point. The uniqueness of Kaprekar's Routine lies in this constant result. Hence, the answer to the math question is that it requires one iteration for the number 6174 to reach its fixed point using the Kaprekar's Routine.

Math Question: Starting with any four-digit number (with at least two different digits), arrange its digits in ascending and descending order to create two new numbers. Subtract the smaller number from the larger number, then repeat the process until the resulting number becomes 6174. How many steps does this process take?

This math concept is known as Kaprekar's Constant, named after Indian mathematician D. R. Kaprekar. The answer to the question is that the process takes exactly 7 steps to reach 6174. Let's demonstrate it: 1. Start with a four-digit number, let's say 6174. 2. Arrange its digits in ascending and descending order: 7641 - 1467 = 6174 3. As the result is already 6174, the process ends since further repetitions will yield the same number. This property of 6174 is quite fascinating, and regardless of the initial number chosen, the process eventually leads to 6174 after at most 7 steps. This intriguing property has captivated mathematicians and is fun to explore!

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

6174 (number)

6174 is an even 4-digits composite number following 6173 and preceding 6175. In scientific notation, it is written as 6.174 × 10^3. The sum of its digits is 18. It has a total of 5 prime factors and 20 positive divisors. There are 1764 positive integers (up to 6174) that are relatively prime to 6174.

Interesting facts

6174 has 20 divisors, whose sum is 14544
The reverse of 6174 is 4716
Previous prime number is 7

Basic properties

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

Name

Name	six thousand one hundred seventy-four

Notation

Scientific notation	6.174 × 10^3
Engineering notation	6.174 × 10^3

Prime Factorization of 6174

Prime Factorization 2 × 21 × 3 × 7 × 7

Composite number

ω	Distinct Factors	4	Total number of distinct prime factors
Ω	Total Factors	5	Total number of prime factors
rad	Radical	882	Product of the distinct prime numbers

The prime factorization of 6174 is 2 × 21 × 3 × 7 × 7. Since it has a total of 5 prime factors.

Most popular turbo-numbers

1, 8, 75, 8, 789, 522, 4664, 3940, 72870, 77957, 998261, 816292, 5081374, 9034857, 571126, 13418611, 926291814, 261813161, 4310892272, 4112885172

Basic calculations (n = 6174)

Multiplication

n×y

n×2	12348
n×3	18522
n×4	24696
n×5	30870

Division

n÷y

n÷2	3087
n÷3	2058
n÷3	1543.5
n÷5	1234.8

Exponentiation

n^y

n²	38118276
n³	235342236024
n⁴	1453002965212176
n⁵	8970840307219974624

Nth Root

^y√n

²√n	78.574805122253
³√n	18.345189759462
⁴√n	8.8642430653865
⁵√n	5.7294551618421

Divisors of 6174

1, 2, 3, 6, 7, 14, 21, 42, 49, 63, 98, 126, 147, 294, 441, 882, 1029, 2058, 3087, 6174

20 divisors

τ	Total Divisors	20	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-6173	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.05	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	20	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 6174 can be divided by 20 positive divisors. The sum of these divisors (counting 6174) is 1, the average is 0.05.

Base conversion 6174

Base	System	Value
2	Binary	1100000011110
3	Ternary	22110200
4	Quaternary	1200132
5	Quinary	144144
6	Senary	44330
8	Octal	14036
10	Decimal	6174
12	Duodecimal	36a6
16	Hexadecimal	181e
20	Vigesimal	f8e
36	Base36	4ri

Cryptographic Hash Functions

md5	65b0df23fd2d449ae1e4b2d27151d73b
sha1	9e7e9aa76105d6a07d98d7be1268e5c9c97cd2d7
sha256	982cba6c0950686e37519d347bfa51deb9c933de7844a3800973b65d78c4667e
sha512	2eca15c9d38a653da67e4fd7014b905757010381a50b567e1a2580c7b396b2c581215308e5e8eea663c4bcdab700c77e58230d2f5c0fa22002310a6740019995
ripemd-160	fca5fc024a00e0cff75b7ca807f291ad71824257

6174 as geometric shapes

Circle

Radius = n

Diameter	12348
Circumference	38792.386086527
Area	119752095.84911

Sphere

Radius = n

Volume	985799253029.86
Surface area	479008383.39643
Circumference	38792.386086527

Square

Length = n

Perimeter	24696
Area	38118276
Diagonal	8731.3545340915

Cube

Length = n

Surface area	228709656
Volume	235342236024
Space diagonal	10693.68168593

Equilateral Triangle

Length = n

Perimeter	18522
Area	16505697.682233
Altitude	5346.8408429651

Triangular Pyramid

Length = n

Surface area	16505697.682233
Volume	27735348498.696
Height	2910.4515113638