Math question: Find the greatest common divisor (GCD) of 1683 and another number such that their sum is a perfect square and their difference is a perfect cube.

To solve this problem, let's assume the other number is N. We want N + 1683 to be a perfect square and N - 1683 to be a perfect cube. To make N + 1683 a perfect square, let's express it as (a + b)², where a and b are positive integers. Expanding this, we get a² + 2ab + b². As we want to match the constant term (1683), we can let b² = 1683. By prime factorizing 1683 = 3 × 19 × 31, we find b = 3 × 19 = 57. Now, a² + 2ab = 0, meaning a(a + 2b) = 0. Since a and b are positive integers, a + 2b = 0 is not possible. So, a = 0, which means N + 1683 = 57² = 3249. Thus, N = 3249 - 1683 = 1566. Next, we want N - 1683 to be a perfect cube. Let's express N - 1683 as (c³), where c is a positive integer. Therefore, c³ = N - 1683 = 1566 - 1683 = -117. Since -117 is not a perfect cube, no solution can be found for this case. Hence, the greatest common divisor of 1683 and another number satisfying the given conditions cannot be determined because no such number exists.

Math question: How many even numbers can be formed using the digits from the number 1683 without repetition?

To form even numbers using the digits 1, 6, 8, and 3 without repetition, we can consider the units place. The digit in the units place must be either 6 or 8 to create even numbers. Therefore, we have 2 choices for the units place. Next, we consider the thousands, hundreds, and tens places. Since these places are filled with 3 different digits (1, 6, and 8), we have 3 choices for the thousands place, 2 choices for the hundreds place, and only 1 choice for the tens place. Hence, the total number of even numbers that can be formed using the digits from 1683 without repetition is: 2 × 3 × 2 × 1 = 12.

Question: What is the square root of 1683, when rounded to the nearest tenth?

The square root of 1683 is approximately 41.0. When squared, it gives 1681, which is the closest perfect square below 1683.

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

1683 (number)

1683 is an odd 4-digits composite number following 1682 and preceding 1684. In scientific notation, it is written as 1.683 × 10^3. The sum of its digits is 18. It has a total of 3 prime factors and 8 positive divisors. There are 960 positive integers (up to 1683) that are relatively prime to 1683.

Interesting facts

1683 has 8 divisors, whose sum is 2160
The reverse of 1683 is 3861
Previous prime number is 11

Basic properties

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

Name

Name	one thousand six hundred eighty-three

Notation

Scientific notation	1.683 × 10^3
Engineering notation	1.683 × 10^3

Prime Factorization of 1683

Prime Factorization 9 × 11 × 17

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	3	Total number of prime factors
rad	Radical	1683	Product of the distinct prime numbers

The prime factorization of 1683 is 9 × 11 × 17. Since it has a total of 3 prime factors.

Most popular turbo-numbers

2, 9, 36, 70, 677, 151, 9880, 3269, 8841, 37269, 358680, 817305, 1674578, 4813613, 35166705, 55006339, 627610014, 574755731, 4499133731, 2650459556

Basic calculations (n = 1683)

Multiplication

n×y

n×2	3366
n×3	5049
n×4	6732
n×5	8415

Division

n÷y

n÷2	841.5
n÷3	561
n÷3	420.75
n÷5	336.6

Exponentiation

n^y

n²	2832489
n³	4767078987
n⁴	8022993935121
n⁵	13502698792808643

Nth Root

^y√n

²√n	41.024382993532
³√n	11.8949157953
⁴√n	6.4050279463506
⁵√n	4.4179095814314

Divisors of 1683

1, 9, 11, 17, 99, 153, 187, 1683

8 divisors

τ	Total Divisors	8	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-1682	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.125	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	8	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1683 can be divided by 8 positive divisors. The sum of these divisors (counting 1683) is 1, the average is 0.125.

Base conversion 1683

Base	System	Value
2	Binary	11010010011
3	Ternary	2022100
4	Quaternary	122103
5	Quinary	23213
6	Senary	11443
8	Octal	3223
10	Decimal	1683
12	Duodecimal	b83
16	Hexadecimal	693
20	Vigesimal	443
36	Base36	1ar

Cryptographic Hash Functions

md5	fddd7938a71db5f81fcc621673ab67b7
sha1	64ff0799c46df444b1554e992807cb15a024846b
sha256	7db67cf8f985b40952938e7402a645eba1d6eecc98fc3166d0be0b47e76dd56c
sha512	faa28d2e91e43c8ce80b101141211b151721270a67b49d7d50fe8986588c03fe9eef991f681b2e21385887f6613d3d33f30cea99a773ec9d1b9fc63733aff33c
ripemd-160	37d8380ba6e7bc1389538bf7686184dbe5879cc8

1683 as geometric shapes

Circle

Radius = n

Diameter	3366
Circumference	10574.600871983
Area	8898526.6337739

Sphere

Radius = n

Volume	19968293766.189
Surface area	35594106.535096
Circumference	10574.600871983

Square

Length = n

Perimeter	6732
Area	2832489
Diagonal	2380.1214254739

Cube

Length = n

Surface area	16994934
Volume	4767078987
Space diagonal	2915.0415091384

Equilateral Triangle

Length = n

Perimeter	5049
Area	1226503.71497
Altitude	1457.5207545692

Triangular Pyramid

Length = n

Surface area	1226503.71497
Volume	561805646.35993
Height	793.37380849131