Prime Numbers

83 and 89

Yes, 45 is an integer number. An integer is a whole number that can be positive, negative, or zero, and it does not have any decimal or fractional parts. In this case, 45 is a positive whole number, making it an integer.

Oh, what a happy little math problem we have here! Let's paint a picture with numbers. If one number is 4 times the other, we can call the smaller number x and the larger number 4x. When we add them together, we get x + 4x = 25. Simplifying that gives us 5x = 25, and when we solve for x, we find that x = 5. So, the two numbers are 5 and 20. Happy little numbers!

Well, isn't that a happy little math problem we have here! Let's see, the two prime numbers that add up to 78 are 41 and 37. Just like in painting, sometimes you need to mix different colors to create something beautiful. Happy calculating!

12 is a composite number, not a prime factor.

No, 301 is not a prime number. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In the case of 301, it can be expressed as 7 x 43, indicating that it has factors other than 1 and itself, making it a composite number.

Well, darling, 11111 times 22222 equals 246864642. But let's be real, who actually multiplies numbers this big without a calculator these days? You must either be a math whiz or just really bored to ask such a question.

Oh, dude, prime numbers are like those special numbers that are only divisible by 1 and themselves. So, between 21 and 40, you've got 23, 29, 31, and 37. They're like the VIP numbers of the math world, you know?

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.