Math question: What is the smallest prime number greater than 2051 that is divisible by 7, 11, and 13?

To find the minimum prime number beginning with 2051, we observe that 2051 is congruent to 5 modulo 7, leaving a remainder of 4. Similarly, it is also 10 modulo 11 (remainder 1) and 3 modulo 13 (remainder 2). To ensure divisibility by all three, we need to keep increasing the number, adding multiples of 1001 since 1001 = 7 × 11 × 13. Evaluating the remainders modulo 7, 11, and 13, we find that the smallest prime number that meets the criteria is 28230983.

Math question: Find the sum of all three-digit numbers between 200 and 300, excluding multiples of 5.

To find the sum, we first calculate the number of terms by subtracting the multiples of 5 between 200 and 300. There are 20 multiples of 5 in this range. Subtracting these multiples from the total number of terms, we have 100 - 20 = 80 three-digit numbers. Since these numbers form an arithmetic sequence with a common difference of 1, the average is the median, which is (200 + 300) / 2 = 250. Hence, the sum is 250 * 80 = 20,000.

Question: What is the remainder when the number 2051 is divided by the sum of its digits?

To find the remainder when 2051 is divided by the sum of its digits, we first calculate the sum of the digits. Adding the digits 2 + 0 + 5 + 1 yields 8. Now, we divide 2051 by 8, which equals 256 with a remainder of 7. Therefore, the remainder is 7.

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

2051 (number)

2051 is an odd 4-digits composite number following 2050 and preceding 2052. In scientific notation, it is written as 2.051 × 10^3. The sum of its digits is 8. It has a total of 2 prime factors and 4 positive divisors. There are 1752 positive integers (up to 2051) that are relatively prime to 2051.

Interesting facts

2051 has 4 divisors, whose sum is 2352
The reverse of 2051 is 1502
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 4
Sum of Digits 8
Digital Root 8

Name

Name	two thousand fifty-one

Notation

Scientific notation	2.051 × 10^3
Engineering notation	2.051 × 10^3

Prime Factorization of 2051

Prime Factorization 7 × 293

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	2	Total number of prime factors
rad	Radical	2051	Product of the distinct prime numbers

The prime factorization of 2051 is 7 × 293. Since it has a total of 2 prime factors.

Most popular turbo-numbers

3, 4, 92, 2, 166, 358, 8582, 6243, 25825, 43522, 625367, 947610, 2421764, 8285075, 78113981, 99491489, 598934706, 579753710, 1645465524, 1111668775

Basic calculations (n = 2051)

Multiplication

n×y

n×2	4102
n×3	6153
n×4	8204
n×5	10255

Division

n÷y

n÷2	1025.5
n÷3	683.66666666667
n÷3	512.75
n÷5	410.2

Exponentiation

n^y

n²	4206601
n³	8627738651
n⁴	17695491973201
n⁵	36293454037035251

Nth Root

^y√n

²√n	45.287967496897
³√n	12.705406175839
⁴√n	6.7296335336255
⁵√n	4.5961387628169

Divisors of 2051

1, 7, 293, 2051

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	-2050	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 2051 can be divided by 4 positive divisors. The sum of these divisors (counting 2051) is 1, the average is 0.25.

Base conversion 2051

Base	System	Value
2	Binary	100000000011
3	Ternary	2210222
4	Quaternary	200003
5	Quinary	31201
6	Senary	13255
8	Octal	4003
10	Decimal	2051
12	Duodecimal	122b
16	Hexadecimal	803
20	Vigesimal	52b
36	Base36	1kz

Cryptographic Hash Functions

md5	a9813e9550fee3110373c21fa012eee7
sha1	33b82c2ed923ebf1beac12f4a41aaf1d4d58b29d
sha256	6f2555e982f65a24613902efb83d1c2a572bc73865dc8bc0b65667b3d792d50f
sha512	687a9d8444650a8e7389fcceed547a9f0b0af81d417d78a04d8e879f88fb349966a426018155d4a95ce505a5fe9997f2f6cd0345d82222bda849497c1ee3b1ea
ripemd-160	60732605c4797cd615f1cce6c78028dff69ba282

2051 as geometric shapes

Circle

Radius = n

Diameter	4102
Circumference	12886.813065025
Area	13215426.798183

Sphere

Radius = n

Volume	36139787150.766
Surface area	52861707.192734
Circumference	12886.813065025

Square

Length = n

Perimeter	8204
Area	4206601
Diagonal	2900.5520164272

Cube

Length = n

Surface area	25239606
Volume	8627738651
Space diagonal	3552.4362063238

Equilateral Triangle

Length = n

Perimeter	6153
Area	1821511.6647925
Altitude	1776.2181031619

Triangular Pyramid

Length = n

Surface area	1821511.6647925
Volume	1016788751.0712
Height	966.85067214241