Math question: If a number, when divided by 5, leaves a remainder of 3, and when divided by 7, leaves a remainder of 1, what is the number?

To find the number, we can use the Chinese Remainder Theorem. Let's solve this step by step. By the Chinese Remainder Theorem, we need to find a common solution to the given equations: 1. n ≡ 3 (mod 5) 2. n ≡ 1 (mod 7) For the first equation, all numbers of the form 5k + 3 satisfy it, where k is an integer. Now let's solve the second equation. All numbers of the form 7m + 1 satisfy it, where m is an integer. To find the common solution, we equate the two forms: 5k + 3 = 7m + 1 Rearranging this and simplifying, we get: 5k - 7m = -2 Now, we need to find an integer solution for k and m. First, observe that k ≡ 1 (mod 7) is a solution since 5(1) - 7(0) = 5 satisfies the equation. So we can write k = 1 + 7t, where t is an integer. Substituting this into the equation, we have: 5(1 + 7t) - 7m = -2 5 + 35t - 7m = -2 35t - 7m = -7 Solving for m, we get m = 5t + 1 for t being an integer. Putting it all together, n ≡ 5k + 3 ≡ 5(1 + 7t) + 3 ≡ 5 + 35t + 3 ≡ 8 + 35t ≡ 8 + 35(5t + 1) ≡ 8 + 175t + 35 ≡ 43 + 175t (mod 35) Hence, the general solution to the problem is n ≡ 43 (mod 35), where n is the number we are searching for. Considering the possible values of n, we find that 43, 78, 113, 148, 183, etc., are solutions. Observing these, we find that the number 2155 satisfies both of the conditions, as 2155 divided by 5 leaves a remainder of 3 and divided by 7 leaves a remainder of 1. Therefore, the number is 2155.

Math Question: If the number 2155 is multiplied by 3 and then divided by 5, what is the result?

To find the result, multiply 2155 by 3, giving us 6465. Then divide 6465 by 5, resulting in 1293. Therefore, the result of multiplying 2155 by 3 and dividing by 5 is 1293.

Math Question: What is the sum of the squares of the prime factors of the number 2155, when each prime factor is raised to the power of its respective digit in the number itself?

To find the answer, let's break down the number 2155. The prime factors of 2155 are 5 and 431. The digits in 2155 are '2', '1', '5', and '5'. Now, we'll calculate the sum of the squares of the prime factors by raising each prime factor to the power of its respective digit and then squaring it. For the digit '2', we have 5^2 (since '2' corresponds to the power) = 25. For digit '1', we have 431^1 = 431. For digits '5' and '5', we have 5^5 = 3125 (as both digits are '5', and so '5' corresponds to the power). Adding up these results, we get 25 + 431 + 3125 = 3581. Hence, the answer is 3581.

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

2155 (number)

2155 is an odd 4-digits composite number following 2154 and preceding 2156. In scientific notation, it is written as 2.155 × 10^3. The sum of its digits is 13. It has a total of 2 prime factors and 4 positive divisors. There are 1720 positive integers (up to 2155) that are relatively prime to 2155.

Interesting facts

2155 has 4 divisors, whose sum is 2592
The reverse of 2155 is 5512
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 4
Sum of Digits 13
Digital Root 4

Name

Name	two thousand one hundred fifty-five

Notation

Scientific notation	2.155 × 10^3
Engineering notation	2.155 × 10^3

Prime Factorization of 2155

Prime Factorization 5 × 431

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	2	Total number of prime factors
rad	Radical	2155	Product of the distinct prime numbers

The prime factorization of 2155 is 5 × 431. Since it has a total of 2 prime factors.

Most popular turbo-numbers

10, 2, 75, 84, 95, 1, 1194, 7720, 71370, 10616, 711581, 854957, 9583393, 1897816, 20138752, 46998080, 908951005, 639069163, 5192025483, 184613381

Basic calculations (n = 2155)

Multiplication

n×y

n×2	4310
n×3	6465
n×4	8620
n×5	10775

Division

n÷y

n÷2	1077.5
n÷3	718.33333333333
n÷3	538.75
n÷5	431

Exponentiation

n^y

n²	4644025
n³	10007873875
n⁴	21566968200625
n⁵	46476816472346875

Nth Root

^y√n

²√n	46.421977553741
³√n	12.916626199434
⁴√n	6.8133675633816
⁵√n	4.641832392732

Divisors of 2155

1, 5, 431, 2155

4 divisors

τ	Total Divisors	4	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-2154	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.25	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	4	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 2155 can be divided by 4 positive divisors. The sum of these divisors (counting 2155) is 1, the average is 0.25.

Base conversion 2155

Base	System	Value
2	Binary	100001101011
3	Ternary	2221211
4	Quaternary	201223
5	Quinary	32110
6	Senary	13551
8	Octal	4153
10	Decimal	2155
12	Duodecimal	12b7
16	Hexadecimal	86b
20	Vigesimal	57f
36	Base36	1nv

Cryptographic Hash Functions

md5	a381c2c35c9157f6b67fd07d5a200ae1
sha1	9d985188444175d30c709f634f65967f67f1ae22
sha256	6ae2718959c46e34ae3c07be90b553c52e64af99c12d7bf41e393247249f25ab
sha512	6030cae94624657ccecd1d514a16c76b25768a91b8a4a3c1162b5df32d7f402b0739dd52c11b5bb79ae404bec7b0b2233fb6a4c770e06bee51908fb46aec1e3e
ripemd-160	445d078d566caef4b3876b6624b88aa208746637

2155 as geometric shapes

Circle

Radius = n

Diameter	4310
Circumference	13540.264336972
Area	14589634.823087

Sphere

Radius = n

Volume	41920884058.338
Surface area	58358539.292349
Circumference	13540.264336972

Square

Length = n

Perimeter	8620
Area	4644025
Diagonal	3047.630226914

Cube

Length = n

Surface area	27864150
Volume	10007873875
Space diagonal	3732.5694903109

Equilateral Triangle

Length = n

Perimeter	6465
Area	2010921.812905
Altitude	1866.2847451555

Triangular Pyramid

Length = n

Surface area	2010921.812905
Volume	1179439247.0454
Height	1015.8767423047