Math Question: A factory produces automobiles, and after one month, they have produced a total of 105 cars. Each subsequent month, the number of cars they produce increases by 15% compared to the previous month. How many cars will the factory produce after 5 months?

To find the number of cars produced after 5 months, we can use exponential growth. Let's denote the initial number of cars as x. After the first month, the factory produces x + 0.15x = 1.15x cars. After the second month, the factory produces 1.15x + 0.15(1.15x) = 1.3225x cars. We can see that the number of cars produced after each month follows the pattern: 1.15^n * x, where n is the number of months. Plugging in n = 5, we get 1.15^5 * x = 1.969x. Therefore, after 5 months, the factory will produce approximately 1.969 times the initial number of cars. Considering the initial production was 105 cars, the factory will produce approximately 206.8 (rounded to the nearest whole number) cars after 5 months.

Question: What is the smallest positive integer greater than 105 that is divisible by 2, 3, 5, and 7 simultaneously?

To find the smallest positive integer satisfying the given divisibility conditions, we can use the concept of the least common multiple (LCM) of the numbers 2, 3, 5, and 7. To calculate the LCM, we start by listing multiples of each number until we find a common multiple. For 2, the multiples are: 2, 4, 6, 8, 10, 12, ... For 3: 3, 6, 9, 12, 15, 18, ... For 5: 5, 10, 15, 20, 25, ... For 7: 7, 14, 21, 28, ... Now, let's find the smallest number that appears in all four lists above. We notice that 105 is a multiple of 3 and 7, so we can eliminate the first few multiples of 3 and 7 and start from 105. The next multiples of 3 and 7 are: 105, 126, 147, 168, ... Checking the list of multiples of 2, we find that 168 (a multiple of 2, 3, and 7) is the smallest common multiple. Hence, the smallest positive integer greater than 105 that is divisible by 2, 3, 5, and 7 simultaneously is 168.

Math Question: Find the sum of all three-digit numbers divisible by 5, but not by 3.

To find the sum, we first determine the range of three-digit numbers divisible by 5. The smallest three-digit number divisible by 5 is 105, and the largest is 195 (200 is not included as it's not a three-digit number). Now, we need to exclude numbers divisible by 3 from this range. Every third multiple of 5 is divisible by 3, so we identify those by finding multiples of 15 within our range. The multiples of 15 between 105 and 195 are 105, 120, 135, 150, 165, 180, and 195. Let's calculate the sum without the multiples of 15. We can see that the set of numbers without multiples of 15 can be written as {105, 110, 115, ..., 195}. This is an arithmetic sequence with a common difference of 5. Using the sum formula, S = (n/2)(a + l), where S is the sum, n is the number of terms, a is the first term, and l is the last term, we can calculate the sum: n = (l - a)/d + 1 = (195 - 105)/5 + 1 = 19 + 1 = 20. Notice that l = 195, a = 105, and d = 5. Thus, S = (20/2)(105 + 195) = 10(300) = 3000. Therefore, the sum of all three-digit numbers divisible by 5 but not by 3 is 3000.

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

105 (number)

105 is an odd 3-digits composite number following 104 and preceding 106. In scientific notation, it is written as 1.05 × 10^2. The sum of its digits is 6. It has a total of 3 prime factors and 8 positive divisors. There are 48 positive integers (up to 105) that are relatively prime to 105.

Interesting facts

105 has 8 divisors, whose sum is 192
The reverse of 105 is 501
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 3
Sum of Digits 6
Digital Root 6

Name

Name	one hundred five

Notation

Scientific notation	1.05 × 10^2
Engineering notation	1.05 × 10^0

Prime Factorization of 105

Prime Factorization 3 × 5 × 7

Composite number

ω	Distinct Factors	3	Total number of distinct prime factors
Ω	Total Factors	3	Total number of prime factors
rad	Radical	105	Product of the distinct prime numbers

The prime factorization of 105 is 3 × 5 × 7. Since it has a total of 3 prime factors.

Most popular turbo-numbers

6, 10, 54, 100, 779, 209, 4617, 5648, 69604, 19348, 711266, 615096, 9932716, 6542345, 75776995, 85246132, 43222184, 552817390, 489486452, 4037982559

Basic calculations (n = 105)

Multiplication

n×y

n×2	210
n×3	315
n×4	420
n×5	525

Division

n÷y

n÷2	52.5
n÷3	35
n÷3	26.25
n÷5	21

Exponentiation

n^y

n²	11025
n³	1157625
n⁴	121550625
n⁵	12762815625

Nth Root

^y√n

²√n	10.24695076596
³√n	4.7176939803165
⁴√n	3.2010858729437
⁵√n	2.5365174816357

Divisors of 105

1, 3, 5, 7, 15, 21, 35, 105

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	-104	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 105 can be divided by 8 positive divisors. The sum of these divisors (counting 105) is 1, the average is 0.125.

Base conversion 105

Base	System	Value
2	Binary	1101001
3	Ternary	10220
4	Quaternary	1221
5	Quinary	410
6	Senary	253
8	Octal	151
10	Decimal	105
12	Duodecimal	89
16	Hexadecimal	69
20	Vigesimal	55
36	Base36	2x

Cryptographic Hash Functions

md5	65b9eea6e1cc6bb9f0cd2a47751a186f
sha1	e114c448f4ab8554ad14eff3d66dfeb3965ce8fc
sha256	1253e9373e781b7500266caa55150e08e210bc8cd8cc70d89985e3600155e860
sha512	03d25c7071bce10d6b462d53854b969d9f61b982e3aee8771bdcca1ecb70495574e6929042f52e859ee9a253b58f776514180ff16e1338f5505e86c7ff328f72
ripemd-160	892375a85d844327330ab1f9c1b6caeb72e77e43

105 as geometric shapes

Circle

Radius = n

Diameter	210
Circumference	659.73445725386
Area	34636.059005827

Sphere

Radius = n

Volume	4849048.2608158
Surface area	138544.23602331
Circumference	659.73445725386

Square

Length = n

Perimeter	420
Area	11025
Diagonal	148.49242404917

Cube

Length = n

Surface area	66150
Volume	1157625
Space diagonal	181.86533479473

Equilateral Triangle

Length = n

Perimeter	315
Area	4773.9650383617
Altitude	90.932667397366

Triangular Pyramid

Length = n

Surface area	4773.9650383617
Volume	136427.41459518
Height	49.497474683058