Prime Numbers

The prime factors of 95 are 5 and 19. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves. In this case, 5 and 19 are the prime numbers that, when multiplied together, equal 95.

Well, isn't that a happy little question! The closest prime number above 200 is 211. Just like adding a touch of bright color to a painting, finding prime numbers can bring a sense of joy and wonder to our mathematical world. Keep exploring and discovering, my friend!

Well, darling, you're out of luck on this one. Prime numbers are only divisible by 1 and themselves, so there's no way to add three of them together to get 56. You might want to brush up on your math facts before trying to stump me next time.

The prime factorization of 7084 is 2^2 x 1771. To find the prime factorization, you would start by dividing 7084 by the smallest prime number, which is 2. After dividing by 2, you get 3542, which can be divided by 2 again to get 1771. 1771 is a prime number, so the prime factorization of 7084 is 2^2 x 1771.

The number between 45 and 60 is 46. When counting between two numbers, you would start at the lower number and increment by one until you reach the higher number. In this case, 45 + 1 = 46, making it the number between 45 and 60.

Oh, what a happy little question! To create a DFA for this set of strings, we can think of states where the number of 0s and 1s seen so far are either divisible by 5 and 3, or not. By transitioning between these states based on the input symbols, we can paint a beautiful DFA that accepts strings with the desired properties. Just remember, there are no mistakes, only happy little accidents in the world of automata!

-19

Well, isn't that just a happy little math problem! To find three numbers that fit these criteria, we can start by placing the median number in the middle, which is 3. Since the mean is also 3, the sum of all three numbers must be 9. By considering the range of 3, we can choose numbers like 2, 3, and 4. This way, we have a mean of 3, a median of 3, and a range of 3. Just like painting, math can be a beautiful and creative process!

Well, isn't that just a happy little math question! Let's take a look at 87 and see what we can find. The prime factors of 87 are 3 and 29. Just like in painting, sometimes it's the little details that come together to create something truly beautiful.

Oh, dude, the prime number closest to 85 is 83. It's like the cool kid at the prime number party, just chillin' next to 85 and keeping it real with its prime factorization of 1 and itself. So yeah, 83 is the prime number you're looking for, no big deal.

The prime numbers between 9 and 15 are 11 and 13. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In this case, 11 and 13 are the only prime numbers within the specified range as 9 is not a prime number because it has divisors other than 1 and itself, and 15 is divisible by 3 and 5 in addition to 1 and 15.

Oh, dude, really? You're hitting me with the math questions? Okay, fine. So, the prime factorization of 803 is 11 x 73. There you go, a little math mixed in with your comedy fix.

There is only one two-digit prime number that has a units digit of 7, and that is 17. This is because all prime numbers greater than 2 are odd, and the only odd prime number ending in 7 within the two-digit range is 17.

43 is the prime you seek. This question is really easy if you know that even numbers larger than 2 are not prime, and that any number ending in 5 is a multiple. The integers greater than 41 and less than 47 are 42,43,44,45, and 46. 42,44,46 are even and 45 is a multiple of 5. Thus 43 is the only candidate. If it factors, is has a prime factor less than 7 since 7 X 7 = 49 and 49 > 43. 2 is not a factor since 43 is odd. 3 is not a factor is the sum of its digits is 7 which is not a multiple of 3. 5 is not a factor since it does not end in 5 .

The number that lies between 1.4 and 2 is 1.5. This number falls exactly halfway between 1.4 and 2 on the number line. It can also be expressed as a fraction, 3/2, which is equivalent to 1.5 in decimal form.

Well, isn't that a happy little math problem! Let's think about it together. The numbers that multiply to make 137 are 1 and 137 because 1 times 137 equals 137. Just like painting a beautiful landscape, sometimes the simplest solutions are the most beautiful.

September has thirty days. Of the numbers 1-30, the following are prime: 2,3,5,7,11,13,17,19,23,29.

The others are composite, except 1 which is neither!

So, 10 primes, 19 composites, and 1

The converse statement for "odd natural numbers less than 8 are prime" would be "prime numbers less than 8 are odd." But honey, just because a number is odd doesn't mean it's automatically prime. Watch out for those sneaky even primes like 2, they'll throw a wrench in your logic party.

To solve this problem, we can use Fermat's Little Theorem, which states that if p is a prime number and a is any integer, then a^p ≡ a (mod p). Given that 29^p + 1 is a multiple of p, we can rewrite this as 29^p ≡ -1 (mod p). This implies that p must be a prime of the form 4k + 1, where k is a non-negative integer. Therefore, there are infinitely many prime numbers p that satisfy the given condition.

The two prime numbers that equal 56 are 2 and 53. 2 is the only even prime number, and 53 is a prime number because it is only divisible by 1 and itself. When multiplied together, 2 x 53 equals 106, not 56. Therefore, there are no two prime numbers that equal 56.

Any number, however, large, that ends in '5' or '0' is divisible by '5'.

Hence 28655 ends in '5' , so it is divisible by '5' . there by it is NOT a prime number.

28655 is a compound number.

5)28655 = 5731

To find the prime factors of 490, we start by dividing it by the smallest prime number, which is 2. 490 ÷ 2 = 245. Next, we divide 245 by the next smallest prime number, which is 5. 245 ÷ 5 = 49. Finally, 49 is a square of 7, which is a prime number. Therefore, the prime factors of 490 are 2 x 5 x 7 x 7.

Well, honey, it's not rocket science. Just start at 2 and keep adding 2 until you hit 100. In programming terms, it's a simple loop that increments by 2 each time until you reach 100. So, get that code going and print those even numbers like a boss!

Oh, what a lovely request! In FoxPro, you can create a program to print all prime numbers from 1 to 100 by using a loop to check each number for divisibility only by 1 and itself. If it meets this criteria, you can print it out on the screen. Remember, every number is unique and special, just like a happy little tree in a vast forest.

The prime factors of 84 are: 2, 3 and 7. So, 2 x 2 x 3 x 7 = 84