Question: What is the smallest positive integer that, when multiplied by 2009, results in a perfect square?

To find the smallest positive integer that yields a perfect square when multiplied by 2009, we must first prime factorize 2009. We get 7 × 7 × 41. For the product to be a perfect square, each prime factor's exponent must be even. Since the exponent for 41 is 1 (an odd number), we need to multiply it with another factor of 41. Thus, the smallest positive integer is 41. When we multiply 41 by 2009, we get 82169, which is indeed a perfect square since it can be expressed as 287^2. Explanation (500 characters): To solve this problem, we employed prime factorization to understand the factors of 2009. By observing that 2009 could be expressed as 7 × 7 × 41, we realized that for the product to be a perfect square, all the prime factors must have even exponents. Since the exponent for factor 41 was 1, we concluded that multiplying it by 41 would make the exponent even (2). Thus, multiplying 41 by 2009 resulted in 82169, which is indeed a perfect square as it can be expressed as 287^2. This approach allowed us to find the smallest positive integer that satisfies the condition.

Question: What is the sum of the prime factors of the number obtained by multiplying 2009 by the product of its digits?

To find the prime factors of 2009, we first multiply it by the product of its digits. The product of the digits is 2 * 0 * 0 * 9 = 0. Thus, the number obtained is 2009 * 0 = 0. As 0 does not have any prime factors, the sum of its prime factors is 0.

Math question: What is the sum of the digits of the product of the prime factors of the number 2009?

To find the prime factors of 2009, we can start by dividing it by 2 repeatedly until we can no longer do so. After finding that 2009/2 = 1004 with a remainder, we continue dividing by prime numbers. Dividing 1004 by 3 gives 334 with no remainder. Further division by 7 yields 47, which is a prime number. So, the prime factors of 2009 are 2, 3, and 7. The product of these factors is 2 * 3 * 7 = 42. Thus, the sum of the digits of 42 is 4 + 2 = 6.

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

2009 (number)

2009 is an odd 4-digits composite number following 2008 and preceding 2010. In scientific notation, it is written as 2.009 × 10^3. The sum of its digits is 11. It has a total of 3 prime factors and 6 positive divisors. There are 1680 positive integers (up to 2009) that are relatively prime to 2009.

Interesting facts

2009 has 6 divisors, whose sum is 2394
The reverse of 2009 is 9002
Previous prime number is 7

Basic properties

Is Prime? no
Number parity odd
Number length 4
Sum of Digits 11
Digital Root 2

Name

Name	two thousand nine

Notation

Scientific notation	2.009 × 10^3
Engineering notation	2.009 × 10^3

Prime Factorization of 2009

Prime Factorization 7 × 7 × 41

Composite number

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	3	Total number of prime factors
rad	Radical	287	Product of the distinct prime numbers

The prime factorization of 2009 is 7 × 7 × 41. Since it has a total of 3 prime factors.

Most popular turbo-numbers

4, 2, 75, 3, 645, 430, 1405, 5259, 79712, 79187, 35892, 978606, 6236077, 8517606, 59198554, 55514474, 173615661, 242118698, 4751568629, 5404483871

Basic calculations (n = 2009)

Multiplication

n×y

n×2	4018
n×3	6027
n×4	8036
n×5	10045

Division

n÷y

n÷2	1004.5
n÷3	669.66666666667
n÷3	502.25
n÷5	401.8

Exponentiation

n^y

n²	4036081
n³	8108486729
n⁴	16289949838561
n⁵	32726509225669049

Nth Root

^y√n

²√n	44.82186966203
³√n	12.618081037132
⁴√n	6.6949137158017
⁵√n	4.5771588763385

Divisors of 2009

1, 7, 41, 49, 287, 2009

6 divisors

τ	Total Divisors	6	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-2008	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.16666666666667	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	6	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 2009 can be divided by 6 positive divisors. The sum of these divisors (counting 2009) is 1, the average is 0.16666666666667.

Base conversion 2009

Base	System	Value
2	Binary	11111011001
3	Ternary	2202102
4	Quaternary	133121
5	Quinary	31014
6	Senary	13145
8	Octal	3731
10	Decimal	2009
12	Duodecimal	11b5
16	Hexadecimal	7d9
20	Vigesimal	509
36	Base36	1jt

Cryptographic Hash Functions

md5	f1981e4bd8a0d6d8462016d2fc6276b3
sha1	7263d678abae47b211a7de6693c9df3ca96d228c
sha256	f37f3f2b0dc57a86dee4ba6ff855283bb4d2f0dea1c5bd1b708853444c2ffcec
sha512	7f856029c0a006af896a52d86071d47f6b0c60933554fd16c4a837d8216f6a1875b69b1c2972f15d59bf517c390f13547da02868d29e0f913c76de86bb9f2a7d
ripemd-160	fd8746eb0df8ed410227799829f58195c4147577

2009 as geometric shapes

Circle

Radius = n

Diameter	4018
Circumference	12622.919282124
Area	12679722.418893

Sphere

Radius = n

Volume	33964749786.076
Surface area	50718889.675573
Circumference	12622.919282124

Square

Length = n

Perimeter	8036
Area	4036081
Diagonal	2841.1550468075

Cube

Length = n

Surface area	24216486
Volume	8108486729
Space diagonal	3479.6900724059

Equilateral Triangle

Length = n

Perimeter	6027
Area	1747674.3388659
Altitude	1739.8450362029

Triangular Pyramid

Length = n

Surface area	1747674.3388659
Volume	955594325.20617
Height	947.05168226918