What is the result when 89 is added to the square root of its product with a number that equals twice the sum of its digits, divided by the difference between the number of factors of 89 and the sum of its digits?

To solve the question, we need to calculate several components. Firstly, the sum of the digits in 89 is (8 + 9) = 17. The number of factors of 89 is 2, as it is a prime number. The product of 89 and 2 times the sum of its digits is (89 * 2 * 17) = 3026. The square root of 3026 is approximately 54.990. The difference between the number of factors of 89 and the sum of its digits is (2 - 17) = -15. Now, dividing 54.990 by -15, we get approximately -3.666. Finally, adding -3.666 to 89 gives us a result of approximately 85.334. Therefore, the answer is approximately 85.334.

Math question: What is the smallest prime number greater than 89 but less than 200?

To find the smallest prime number greater than 89 but less than 200, we need to check each number within this range if it is divisible by any number other than 1 and itself. Starting from 90, we notice that 91 is divisible by 7 (since 7 x 13 = 91), hence it is not prime. We continue our search until we find a number that is not divisible by any number other than 1 and itself. By checking each subsequent number, we find that 97 is the first number that meets this criteria. Therefore, 97 is the smallest prime number greater than 89 but less than 200.

Question: What is the sum of consecutive odd integers, starting from 89, up to the number of terms that make the sum equal to or greater than 7000?

Let's solve the problem step by step. The first odd integer is 89. We can represent the subsequent odd integers as 89 + 2n, where n represents the number of terms. The sum of these integers can be expressed as S = (n/2)(89 + 89 + 2n - 2) = (n/2)(4n + 176). We want to find the smallest value of n that satisfies S >= 7000. Setting up this inequality, we have (n/2)(4n + 176) >= 7000. Simplifying it further, we get 2n^2 + 88n - 7000 >= 0. By factoring or using the quadratic formula, we find that n >= 29. Thus, to make the sum equal to or greater than 7000, we need at least 29 terms. The sum of the consecutive odd integers from 89 to 89 + 2(29-1) = 245 is 7000.

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

89 (number)

89 is an odd 2-digits prime number following 88 and preceding 90. In scientific notation, it is written as 8.9 × 10^1. The sum of its digits is 17. It has a total of 1 prime factors and 2 positive divisors. There are 88 positive integers (up to 89) that are relatively prime to 89.

Interesting facts

89 has 2 divisors, whose sum is 90
The reverse of 89 is 98
Previous prime number is 1

Basic properties

Is Prime? yes
Number parity odd
Number length 2
Sum of Digits 17
Digital Root 8

Name

Name	eighty-nine

Notation

Scientific notation	8.9 × 10^1
Engineering notation	8.9 × 10^0

Prime Factorization of 89

Prime Factorization 89

Composite number

ω	Distinct Factors	1	Total number of distinct prime factors
Ω	Total Factors	1	Total number of prime factors
rad	Radical	89	Product of the distinct prime numbers

The prime factorization of 89 is 89. Since it has a total of 1 prime factors.

Most popular turbo-numbers

9, 8, 57, 42, 647, 324, 608, 706, 83387, 50934, 813765, 611738, 9651269, 6687502, 91563008, 9216187, 869540601, 521670298, 5434201653, 6085918506

Basic calculations (n = 89)

Multiplication

n×y

n×2	178
n×3	267
n×4	356
n×5	445

Division

n÷y

n÷2	44.5
n÷3	29.666666666667
n÷3	22.25
n÷5	17.8

Exponentiation

n^y

n²	7921
n³	704969
n⁴	62742241
n⁵	5584059449

Nth Root

^y√n

²√n	9.4339811320566
³√n	4.4647450955845
⁴√n	3.0714786556407
⁵√n	2.4540194545491

Divisors of 89

1, 89

2 divisors

τ	Total Divisors	2	Total number of the positive divisors of n
σ	Sum of Divisors	90	Sum of all the positive divisors of n
s	Aliquot Sum	1	Sum of the proper positive divisors of n
A	Arithmetic Mean	45	Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n))
G	Geometric Mean	9.4868329805051	Returns the nth root of the product of n divisors
H	Harmonic Mean	1.9777777777778	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 89 can be divided by 2 positive divisors. The sum of these divisors (counting 89) is 90, the average is 45.

Base conversion 89

Base	System	Value
2	Binary	1011001
3	Ternary	10022
4	Quaternary	1121
5	Quinary	324
6	Senary	225
8	Octal	131
10	Decimal	89
12	Duodecimal	75
16	Hexadecimal	59
20	Vigesimal	49
36	Base36	2h

Cryptographic Hash Functions

md5	7647966b7343c29048673252e490f736
sha1	16b06bd9b738835e2d134fe8d596e9ab0086a985
sha256	cd70bea023f752a0564abb6ed08d42c1440f2e33e29914e55e0be1595e24f45a
sha512	a3f1d1838dfbe3d28a3b5eb40c36c175c051d2eafe9f6a3dd714ca0d221754a91c016cf93cba110bcd09848287dbd7ec0dee3f676c588f830af33b45d845573c
ripemd-160	5fe81cda018fbe2426459475a30a1f08c15de224

89 as geometric shapes

Circle

Radius = n

Diameter	178
Circumference	559.20349233898
Area	24884.555409085

Sphere

Radius = n

Volume	2952967.2418781
Surface area	99538.221636339
Circumference	559.20349233898

Square

Length = n

Perimeter	356
Area	7921
Diagonal	125.86500705121

Cube

Length = n

Surface area	47526
Volume	704969
Space diagonal	154.15252187363

Equilateral Triangle

Length = n

Perimeter	267
Area	3429.8936116883
Altitude	77.076260936815

Triangular Pyramid

Length = n

Surface area	3429.8936116883
Volume	83081.393404383
Height	41.955002350402