The numbers 211, 223, 227, 229, 233, 239 and 241 are prime.

11

13, 31

17, 71

37, 73

79, 97

315

Well, honey, XXVI is Roman numerals for 26. It's like saying "I'm feeling 26" in Roman times. So, if you ever need to impress someone with your knowledge of ancient numbering systems, you're all set.

Well, let's take a moment to appreciate the beauty of a number line. If we start at 2 and move 5 units to the left, we end up at -3. Remember, on a number line, moving to the right means adding and moving to the left means subtracting. Just a happy little journey on the number line!

There is ONly ONE prime number that is EVEN. It is TWO(2).

All other prime numbers to infinity are odd.

Oh, dude, let me break it down for you. So, the numbers that go into 601 are 1, 601, and themselves. Yeah, that's it. Like, it's a prime number, so it's pretty exclusive, you know? It's like the VIP section of numbers.

No, 2x2x2x3x5x5 is not a prime factorization. A prime factorization is a representation of a number as a product of prime numbers. In this case, 2x2x2x3x5x5 can be simplified to 2^3 x 3 x 5^2, which is the prime factorization of the number.

Oh, dude, you're talking about four-digit numbers where every digit is even, right? So, we've got 2, 4, 6, and 8 to play with. Each place can have any of those four options, so it's like 4 choices for each of the 4 digits. That's 4x4x4x4, which is 256 numbers between 1000 and 9999 where all the digits are even.

Oh, dude, the positive difference between the number of distinct prime factors of 15 squared (225) and 64 cubed (262,144) is like 4. Prime factors are like those VIP numbers that can't be divided by anything except 1 and themselves. So, 225 has 2 distinct prime factors (3 and 5), and 262,144 has 1 distinct prime factor (2). Subtract 1 from 2, and you get 1. Wow, math can be fun, right?

'15'

Hence

3 x 5 = 15

or

15/3 = 5

or

15/5 = 3

The prime factors of 180 are the prime numbers that can be multiplied together to equal 180. To find the prime factors of 180, we start by dividing 180 by the smallest prime number, which is 2. Continuing this process, we find that the prime factors of 180 are 2, 2, 3, 3, and 5, represented as 2^2 * 3^2 * 5.

Oh, what a happy little question! Adding numbers 1 through 250 together is like creating a beautiful painting with all the colors of the rainbow. The total sum is 31,375, a lovely number that shows how each little number can come together to make something truly wonderful. Just like how each brushstroke adds to the beauty of a painting, each number adds to the magic of mathematics.

2.5#

where # is any number, at least one digit except all zeros

examples:

2.56

2.5999

2.56123789

2.5215791238154

2.5000000000000000000000000000000000001

The prime numbers that add up to 70 are 3, 11, 13, 17, and 19. These prime numbers are indivisible by any number other than 1 and themselves. When added together, they equal 70, which is the sum of all the prime numbers mentioned.

Oh, dude, you're hitting me with the math questions now? Alright, so 39 can be broken down into 3 x 13. So, like, 3 and 13 are the prime numbers that, when multiplied together, give you 39. It's like breaking down a secret code, but with numbers.

Well, honey, let me break it down for you. Two even numbers can never be relatively prime because they will always have a common factor of 2. So, technically speaking, they can't be besties in the world of prime numbers. But hey, at least they can still hang out at the even number party together.

The number 44 is not a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In the case of 44, it can be divided evenly by numbers other than 1 and 44, such as 2, 4, 11, and 22. Therefore, 44 does not meet the criteria of a prime number.

The prime factorization of 25n^2 is 5 * 5 * n * n, or simply 5^2 * n^2. This means that the prime factors of 25n^2 are 5 and n, each raised to the power of 2. In other words, 25n^2 can be expressed as the product of 5 squared and n squared.

Oh honey, 84 is just begging to be broken down. In exponential form, you've got 2^2 * 3^1 * 7^1. It's like a math party, and 84 is the guest of honor!

-98

Oh, dude, that's like a fun little math game you got there! So, if you look closely, you'll notice that each number is just the sum of the previous number and the position in the sequence. It's like a math puzzle for your brain to solve while you're waiting for your pizza delivery. Enjoy!

Well, honey, when you divide a number by something smaller than one, you're essentially multiplying it. It's like sharing a pizza with fewer people - you end up with more slices. So, technically speaking, the number gets larger because math says so.

2 and 7 is the only such pair.