Math question: What is the sum of the first 100 positive even integers greater than 1002?

To find the sum of the first 100 positive even integers greater than 1002, we can use the arithmetic series formula. The first term, a₁, is 1002 + 2 = 1004 (since we start with the first even integer that is greater than 1002) and the common difference, d, is 2 (since we are dealing with even numbers). We want to find the sum of the first 100 terms, so n (the number of terms) is 100. Plugging these values into the formula Sₙ = (n/2)(2a₁ + (n-1)d), we get Sₙ = (100/2)(2(1004) + (100-1)(2)). Simplifying this further, Sₙ = 50(2008 + 198). Hence, the sum of the first 100 positive even integers greater than 1002 equals 103,400.

Math question: What is the result when 1002 is multiplied by the sum of the digits in its hundred and tens places, divided by the difference between the units digit and the tens digit, then subtracted by the square root of the cubes of the hundreds and units digits?

First, observe that the sum of the digits in the hundred and tens places of 1002 is 1 + 0 = 1. The units digit is 2. Therefore, the difference between the units and tens digit is 2 - 0 = 2. Taking the square root of the cubes of the hundreds and units digits is equal to taking the square root of (1^3 + 2^3) = √(1 + 8) = √9 = 3. Now, let's evaluate the expression: 1002 × (1 / 2) - 3 = 1002 × 0.5 - 3 = 501 - 3 = 498. Thus, the result when 1002 is multiplied by the sum of the digits in its hundred and tens places, divided by the difference between the units digit and the tens digit, then subtracted by the square root of the cubes of the hundreds and units digits, is 498.

Math Question: If 1002 is divided by x, multiplied by y, and then subtracted by z, the result is equal to 500. Find the values of x, y, and z.

Let's solve the equation step by step: 1002 / x * y - z = 500. First, rearranging the equation, we get 1002 * y - z * x = 500 * x. Since y and z are not mentioned, let's assume arbitrary values, y = 2 and z = 100. Now, we have the equation 1002 * 2 - 100 * x = 500 * x. Simplifying it further, 2004 - 100x = 500x. Combining like terms, 500x + 100x = 2004. Simplifying, 600x = 2004. Dividing both sides by 600, we find x = 3.34. Thus, the values of x, y, and z that satisfy the equation are x = 3.34, y = 2, and z = 100.

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

1002 (number)

1002 is an even 4-digits composite number following 1001 and preceding 1003. In scientific notation, it is written as 1.002 × 10^3. The sum of its digits is 3. It has a total of 3 prime factors and 8 positive divisors. There are 332 positive integers (up to 1002) that are relatively prime to 1002.

Interesting facts

1002 has 8 divisors, whose sum is 2016
The reverse of 1002 is 2001
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 4
Sum of Digits 3
Digital Root 3

Name

Name	one thousand two

Notation

Scientific notation	1.002 × 10^3
Engineering notation	1.002 × 10^3

Prime Factorization of 1002

Prime Factorization 2 × 3 × 167

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	3	Total number of prime factors
rad	Radical	1002	Product of the distinct prime numbers

The prime factorization of 1002 is 2 × 3 × 167. Since it has a total of 3 prime factors.

Most popular turbo-numbers

4, 5, 18, 98, 832, 682, 7881, 9149, 45607, 93947, 354604, 923890, 5334214, 9148979, 72710679, 71032784, 408712714, 321173269, 7825529946, 8815870185

Basic calculations (n = 1002)

Multiplication

n×y

n×2	2004
n×3	3006
n×4	4008
n×5	5010

Division

n÷y

n÷2	501
n÷3	334
n÷3	250.5
n÷5	200.4

Exponentiation

n^y

n²	1004004
n³	1006012008
n⁴	1008024032016
n⁵	1010040080080032

Nth Root

^y√n

²√n	31.654383582689
³√n	10.006662227154
⁴√n	5.6262228522063
⁵√n	3.9826628618008

Divisors of 1002

1, 2, 3, 6, 167, 334, 501, 1002

8 divisors

τ	Total Divisors	8	Total number of the positive divisors of n
σ	Sum of Divisors	1	Sum of all the positive divisors of n
s	Aliquot Sum	-1001	Sum of the proper positive divisors of n
A	Arithmetic Mean	0.125	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	8	Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors

The number 1002 can be divided by 8 positive divisors. The sum of these divisors (counting 1002) is 1, the average is 0.125.

Base conversion 1002

Base	System	Value
2	Binary	1111101010
3	Ternary	1101010
4	Quaternary	33222
5	Quinary	13002
6	Senary	4350
8	Octal	1752
10	Decimal	1002
12	Duodecimal	6b6
16	Hexadecimal	3ea
20	Vigesimal	2a2
36	Base36	ru

Cryptographic Hash Functions

md5	fba9d88164f3e2d9109ee770223212a0
sha1	a5b1d7e217aa227d5b2b8a84920780cf637960e2
sha256	b281bc2c616cb3c3a097215fdc9397ae87e6e06b156cc34e656be7a1a9ce8839
sha512	59963bfd1fef9ea453959517c8755d00cfa0d7c57f112404f3ca9def63986c149d9aabb28ccb225b5a3470e42a170141558d6d6b87ff104931c754fad0d5c933
ripemd-160	079db7ddfbc5c137f1bd3ea2d455f9fa21b0f38a

1002 as geometric shapes

Circle

Radius = n

Diameter	2004
Circumference	6295.7516777939
Area	3154171.5905748

Sphere

Radius = n

Volume	4213973245.0079
Surface area	12616686.362299
Circumference	6295.7516777939

Square

Length = n

Perimeter	4008
Area	1004004
Diagonal	1417.0419894978

Cube

Length = n

Surface area	6024024
Volume	1006012008
Space diagonal	1735.514909184

Equilateral Triangle

Length = n

Perimeter	3006
Area	434746.4847506
Altitude	867.75745459201

Triangular Pyramid

Length = n

Surface area	434746.4847506
Volume	118559652.13532
Height	472.34732983261