Prime Numbers

The smallest prime number greater than 100 is 101. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In this case, 101 is indivisible by any other numbers except for 1 and 101, making it a prime number.

To find the largest odd natural number that is a factor of 120, we first need to factorize 120 into its prime factors, which are 2^3 * 3 * 5. Since we are looking for an odd factor, we can ignore the factor of 2. The largest odd factor of 120 is then 3, as it is the largest odd prime factor present in the prime factorization of 120.

Oh, dude, 1 and 1665 go into 1665. Like, that's it. Easy peasy lemon squeezy.

Any number that is 11 or less is less than or equal to 11. This includes all whole numbers from 1 to 11, as well as any decimal or fraction less than 11. In mathematical notation, this can be represented as x ≤ 11, where x is the number in question.

Let n be an arbitrary natural number.

The next larger natural number is n + 1.

The sum of these natural numbers is n + (n + 1)

n + (n + 1) = 525

2n + 1 = 525

2n = 524

n = 262

n + 1 = 263.

The two natural numbers are 262 and 263.

Oh, dude, consecutive numbers are just numbers that come right after each other, like they're holding hands or something. So, for 4422, the consecutive numbers would be 4421 and 4423. It's like a little number sandwich, but with a missing slice of bread.

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The two numbers that have a product of 30 and a sum of 9 are 3 and 10. This is because 3 multiplied by 10 equals 30, and 3 plus 10 equals 13. Since the sum of the numbers is 9, we can deduce that 3 and 10 are the correct pair of numbers that satisfy both conditions simultaneously.

The prime factorization of 2x2x3x3x5 is 2^2 * 3^2 * 5. When we multiply these prime factors together, we get the number 180. Therefore, the number with the prime factorization of 2x2x3x3x5 is 180.

The number 64 is a composite number, as it can be divided evenly by numbers other than 1 and itself, such as 2, 4, 8, 16, and 32. It is the square of 8, as 8 multiplied by 8 equals 64. In binary code, 64 is represented as 100000. Additionally, 64 is a perfect square and a cube.

No. A prime number is a number only divisible by one and itself. 91/7 = 13.

The first twenty-five prime numbers include 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

The prime factorization of 252 is 2^2 * 3^2 * 7. This means that 252 can be expressed as the product of these prime factors raised to their respective powers. In exponential form, this would be written as 2^2 * 3^2 * 7.

Numbers with exactly 6 factors are perfect squares of prime numbers. The prime factorization of a number with exactly 6 factors is in the form ( p^2 ), where ( p ) is a prime number. There are 10 prime numbers less than 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. So, there are 10 numbers less than 30 that have exactly 6 factors.

Oh honey, 861 is about as composite as a Kardashian selfie. It can be divided by 1, 3, 7, 17, 21, 51, 119, and 357. So, unless you're looking for a prime number to make your day, 861 is definitely not it.

List the primes up to 20 (2, 3, 5, 7, 11, 13, 17, 19) and note that the largest possible prime in the sum is 13 because no two primes add up to and of course 19 is too large as well. Also, observe that 2, the only even prime, must be in the sum, because the sum of three odd primes cannot never be 20. Starting with 2 and 3, we see that is not prime. Next, 2 and 5 give , a prime, so one such increasing sequence is 2, 5, 13. Next, we take 2 and 7, and we see that is prime as well, giving us the second sequence 2, 7, 11. 11 and 13 are already included, so we are done. Thus, there are increasing sequences of three distinct prime numbers that have a sum of 20.

Some examples are:

the square root of any integer between 192 and 202, or

the cube root of any integer between 193 and 203, or

the fourth root of any integer between 194 and 204.

Oh, dude, there are like 899 numbers between 100 and 999. You just subtract the starting number from the ending number, but hey, who's counting? Oh wait, we are, literally.

Well, well, well, look at you trying to stump me. The prime numbers less than 30 that multiply to 1955 are 5, 13, and 31. Yep, you heard me right, 31 is not less than 30, but it sure is a prime number that gets the job done.

I'll build the numbers with prime divisors

2 = 2 so 2

3 = 3 so 2 x 3

4 = 2 x 2 so 2 x 2 x 3

5 = 5 so 2 x 2 x 3 x 5

We already have 6 because 6 = 2 x 3 so we leave it like that

7 = 7 so 2 x 2 x 3 x 5 x 7

8 = 2 x 2 x 2 so 2 x 2 x 2 x 3 x 5 x 7

9 = 3 x 3 so 2 x 2 x 2 x 3 x 3 x 5 x 7

We already have 10 because 10 = 2 x 5

11 = 11 so 2 x 2 x 2 x 3 x 3 x 5 x 7 x 11

We already have 12 because 12 = 2 x 2 x 3 so we're done

SCM = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 11 = 27720

The smallest common multiple of every number from 1 to 12 is 27720. However it's also the smallest common multiple of every number from 1 to 11 because 11 was the last prime or prime power we added so we can ignore 12 if we want

The prime factorization of 42 is 2 x 3 x 7. In index form, this can be written as 2^1 x 3^1 x 7^1. This means that 42 can be expressed as the product of these prime numbers, each raised to the power of 1.

The factors of 1000000000 are the numbers that can be multiplied together to result in 1000000000. These factors include 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 625, 800, 1000, 1250, 1600, 2000, 2500, 3125, 4000, 5000, 6250, 8000, 10000, 12500, 20000, 25000, 40000, 50000, 100000, 125000, 200000, 250000, 500000, and 1000000. The prime factors of 1000000000 are the prime numbers that can be multiplied together to result in 1000000000, which are 2, 5.

There are 11 even numbers between 17 and 39. To find this, we first determine the even numbers between 17 and 39 are 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, and 38. We can calculate this by subtracting the first even number (18) from the last even number (38) and then adding 2 (since we are counting inclusive of both endpoints).

counting numbers greater than 1but less than 10 = 2, 3, 4, 5, 6, 7, 9

Well, isn't prime factorization just a beautiful way to break down a number into its simplest parts? Let's take 48, for example. We can express it as 2 x 2 x 2 x 2 x 3, where 2 and 3 are prime numbers. It's like finding the unique colors in a painting, each prime factor is like a special hue that makes up the whole picture.

Oh, dude, expressing 294 as the product of prime factors is like breaking down a complicated relationship. You start by dividing 294 by the smallest prime number, which is 2. Then you keep going until you can't divide anymore. In the end, you'll have 2 x 3 x 7 x 7, which is the prime factorization of 294. Easy peasy lemon squeezy!