Question 1

Math question: What is the sum of all the digits in the number 2001?

Accepted Answer

To find the sum of all the digits in the number 2001, we break it down into individual digits. The digit 2 occurs once, the digit 0 occurs twice, and the digit 1 occurs once. Adding these individual digits together, we get 2 + 0 + 0 + 1 = 3. Therefore, the sum of all the digits in the number 2001 is 3.

Explanation: The number 2001 consists of four digits: 2, 0, 0, and 1. When summing the digits, we separately consider each digit. The digit 2 occurs once, so we have 2. Next, the digit 0 appears twice, leading to 0 + 0 = 0. Lastly, the digit 1 occurs once, so we have 1. Adding all these individual sums together gives us 2 + 0 + 0 + 1 = 3. Thus, the sum of all the digits in the number 2001 is 3.

Question 2

Math question: What is the sum of all odd multiples of 9 between 2001 and 4000?

Accepted Answer

To find the sum of odd multiples of 9 between 2001 and 4000, we first find the smallest odd multiple of 9 greater than or equal to 2001, which is 2001 itself. The largest odd multiple of 9 less than or equal to 4000 is 3993. To find the number of terms in this arithmetic sequence, we use the formula:

nth term = first term + (n - 1) * common difference,

where nth term is the last term in the sequence, the first term is 2001, and the common difference is 18 (9 times 2 since we are considering odd multiples). Rearranging the formula, we have:

n = (nth term - first term) / common difference + 1

n = (3993 - 2001) / 18 + 1 = 111.

Now, using the formula for the sum of an arithmetic series:

Sum = (n / 2) * (first term + last term) = (111 / 2) * (2001 + 3993) = 55.5 * 5994 = 331,437.

Therefore, the sum of all odd multiples of 9 between 2001 and 4000 is 331,437.

Question 3

Math question:
What is the sum of all odd four-digit numbers greater than or equal to 2001 if we skip every multiple of 47?

Accepted Answer

To find the sum of odd four-digit numbers greater than or equal to 2001 while excluding every multiple of 47, we should first determine the number of odd four-digit numbers beyond 2001.

The smallest odd four-digit number greater than 2001 is 2003, and the largest is 9999. To find how many numbers are in this sequence, we can calculate the number of odd numbers in the full range from 2001 to 9999 and then subtract all the multiples of 47.

The first odd number in the range is 2001, and the last even number is 9999. To calculate the number of odd integers in this arithmetic sequence, we employ the formula:

n = (last term - first term) / common difference + 1

For our sequence, the common difference is 2 since we are dealing with odd numbers. Plugging in the values, we get:

n = (9999 - 2001) / 2 + 1
= 3999 / 2 + 1
= 1999 + 1
= 2000

Thus, there are 2000 odd four-digit numbers beyond 2001.

Next, we need to determine the number of multiples of 47 within this range. To find this, we can calculate the largest and smallest multiples of 47 in this range and count the number of terms.

The smallest multiple of 47 greater than or equal to 2001 is 2016 (with the quotient 42), whereas the largest multiple of 47 less than or equal to 9999 is 9919 (with the quotient 211).

Again, using the arithmetic sequence formula, we find the number of terms:

n = (last term - first term) / common difference + 1

n = (9919 - 2016) / 47 + 1
= 7903 / 47 + 1
= 167 + 1
= 168

Hence, there are 168 multiples of 47 within the given range.

Now, since there are 2000 odd four-digit numbers and we need to exclude 168 multiples of 47, we have 2000 - 168 = 1832 odd four-digit numbers that are not multiples of 47.

To find the sum of this sequence, we can use the arithmetic series formula:

Sum = (n/2)(first term + last term)

Sum = (1832/2)(2003 + (2003 + (1832 - 1) * 2))
= 916(2003 + 3662)
= 916(5665)
= 5,184,860

Therefore, the sum of all odd four-digit numbers greater than or equal to 2001 while excluding every multiple of 47 is 5,184,860.

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

Scientific notation	2.001 × 10^3
Engineering notation	2.001 × 10^3

ω	Distinct Factors	2	Total number of distinct prime factors
Ω	Total Factors	2	Total number of prime factors
rad	Radical	2001	Product of the distinct prime numbers

n×2	4002
n×3	6003
n×4	8004
n×5	10005

n÷2	1000.5
n÷3	667
n÷3	500.25
n÷5	400.2

2001 (number)

Interesting facts

Basic properties

Name

Notation

Prime Factorization of 2001

Most popular turbo-numbers

Basic calculations (n = 2001)

Multiplication

Division

Exponentiation

Nth Root

Divisors of 2001

Base conversion 2001

Cryptographic Hash Functions

2001 as geometric shapes

Circle

Sphere

Square

Cube

Equilateral Triangle

Triangular Pyramid

n²	4004001
n³	8012006001
n⁴	16032024008001
n⁵	32080080040010001

²√n	44.73253849269
³√n	12.601310017484
⁴√n	6.6882388184551
⁵√n	4.5735077328916

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	-2000	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

Base	System	Value
2	Binary	11111010001
3	Ternary	2202010
4	Quaternary	133101
5	Quinary	31001
6	Senary	13133
8	Octal	3721
10	Decimal	2001
12	Duodecimal	11a9
16	Hexadecimal	7d1
20	Vigesimal	501
36	Base36	1jl

md5	d0fb963ff976f9c37fc81fe03c21ea7b
sha1	9195f873d1715b7575f88118db6dc42a91137874
sha256	85d6385b945c0d602103db39b0b654b2af93b5127938e26a959c123f0789b948
sha512	3e21cfcddff13e45bad872906ef560e7737ffb53abe7060c360603a80960db0eaa269b368a93f14a4323bada701320eae435ffba0441185698fe433145b7e1b3
ripemd-160	a1681edd51ce6a217be534e1c5f95522c9ef7d5b

Volume	33560612257.679
Surface area	50315760.506265
Circumference	12572.653799666

Surface area	24024006
Volume	8012006001
Space diagonal	3465.8336659453

Surface area	1733783.2913891
Volume	944223962.36907
Height	943.28044610285

Diameter	4002
Circumference	12572.653799666
Area	12578940.126566

Perimeter	8004
Area	4004001
Diagonal	2829.8413383086

Perimeter	6003
Area	1733783.2913891
Altitude	1732.9168329727