Math question: What is the sum of all multiples of 7 between 1301 and 2000?

To find the sum, we need to determine the number of multiples of 7 and then calculate their sum. The first multiple of 7 greater than or equal to 1301 is 1302. The last multiple less than or equal to 2000 is 1995. We can apply the formula (last term - first term) / common difference + 1 to find the number of terms: (1995 - 1302) / 7 + 1 = 85. Now, we can calculate the sum using the formula: sum = (n/2)(first term + last term), where n represents the number of terms. Plugging in the values, we have: sum = (85/2)(1302 + 1995) = 645 * 3297 = 2,128,265. Thus, the sum of all multiples of 7 between 1301 and 2000 is 2,128,265.

Question: What is the smallest prime number greater than 1301 that, when divided by 7, leaves a remainder of 1, and when divided by 13, leaves a remainder of 5?

To find the smallest prime number that satisfies the given conditions, we need to check the numbers greater than 1301. Starting from 1302, we check numbers that leave a remainder of 1 when divided by 7 and a remainder of 5 when divided by 13. After checking a few numbers, we find that 1319 meets the criteria. Now, we need to verify if 1319 is a prime number. We can check if it's divisible by any prime numbers less than its square root. By dividing it by small primes (2, 3, 5, 7), we see that it is not divisible. Hence, we can confirm that 1319 is a prime number. Thus, the smallest prime number greater than 1301 that leaves a remainder of 1 when divided by 7 and a remainder of 5 when divided by 13 is 1319.

What is the smallest prime number greater than 1301?

The smallest prime number greater than 1301 is 1303. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. To determine the smallest prime number greater than 1301, we can start by checking if any numbers greater than 1301 are divisible by any numbers other than 1 and themselves. After checking, we find that 1303 is the smallest prime number greater than 1301.

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

1301 (number)

1301 is an odd 4-digits prime number following 1300 and preceding 1302. In scientific notation, it is written as 1.301 × 10^3. The sum of its digits is 5. It has a total of 1 prime factors and 2 positive divisors. There are 1300 positive integers (up to 1301) that are relatively prime to 1301.

Interesting facts

1301 has 2 divisors, whose sum is 1302
The reverse of 1301 is 1031
Previous prime number is 1

Basic properties

Is Prime? yes
Number parity odd
Number length 4
Sum of Digits 5
Digital Root 5

Name

Name	one thousand three hundred one

Notation

Scientific notation	1.301 × 10^3
Engineering notation	1.301 × 10^3

Prime Factorization of 1301

Prime Factorization 1301

Composite number

ω	Distinct Factors	1	Total number of distinct prime factors
Ω	Total Factors	1	Total number of prime factors
rad	Radical	1301	Product of the distinct prime numbers

The prime factorization of 1301 is 1301. Since it has a total of 1 prime factors.

Most popular turbo-numbers

10, 1, 69, 88, 586, 162, 7885, 3344, 35917, 30133, 453602, 902513, 5055342, 212926, 39661389, 97617901, 179206822, 740862353, 5125632197, 4681212187

Basic calculations (n = 1301)

Multiplication

n×y

n×2	2602
n×3	3903
n×4	5204
n×5	6505

Division

n÷y

n÷2	650.5
n÷3	433.66666666667
n÷3	325.25
n÷5	260.2

Exponentiation

n^y

n²	1692601
n³	2202073901
n⁴	2864898145201
n⁵	3727232486906501

Nth Root

^y√n

²√n	36.069377593743
³√n	10.916726556658
⁴√n	6.0057786833801
⁵√n	4.1961930421273

Divisors of 1301

1, 1301

2 divisors

τ	Total Divisors	2	Total number of the positive divisors of n
σ	Sum of Divisors	1302	Sum of all the positive divisors of n
s	Aliquot Sum	1	Sum of the proper positive divisors of n
A	Arithmetic Mean	651	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	36.083237105337	Returns the nth root of the product of n divisors
H	Harmonic Mean	1.9984639016897	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1301 can be divided by 2 positive divisors. The sum of these divisors (counting 1301) is 1302, the average is 651.

Base conversion 1301

Base	System	Value
2	Binary	10100010101
3	Ternary	1210012
4	Quaternary	110111
5	Quinary	20201
6	Senary	10005
8	Octal	2425
10	Decimal	1301
12	Duodecimal	905
16	Hexadecimal	515
20	Vigesimal	351
36	Base36	105

Cryptographic Hash Functions

md5	2df45244f09369e16ea3f9117ca45157
sha1	055550dad2fd7bb5aee434f17ca74ca072982ac1
sha256	0f2cb44170f42cc966535f392a10dcd4499426df69dc476f1bf36609f7fa8c1e
sha512	5bd7343579ca2dbf14076d93a60abd704dd493786ccb539f399e3bcf0c796e07da93e646521f9d069b2375b49c84afaebc554120fc9b85ba232e1ba6d6db8af4
ripemd-160	0b4ab1fcf0e7f5dc73bffc6e5767699bed76f4d7

1301 as geometric shapes

Circle

Radius = n

Diameter	2602
Circumference	8174.4240846406
Area	5317462.8670587

Sphere

Radius = n

Volume	9224025586.7246
Surface area	21269851.468235
Circumference	8174.4240846406

Square

Length = n

Perimeter	5204
Area	1692601
Diagonal	1839.8918446474

Cube

Length = n

Surface area	10155606
Volume	2202073901
Space diagonal	2253.3981006471

Equilateral Triangle

Length = n

Perimeter	3903
Area	732917.73223547
Altitude	1126.6990503236

Triangular Pyramid

Length = n

Surface area	732917.73223547
Volume	259516898.01184
Height	613.29728154913