Prime Numbers

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.

The prime factorization of 1955 is 5 x 17 x 23. To find three prime numbers whose product is 1955, we need to find a combination of these prime factors that multiply to 1955. The prime numbers less than 30 that can be formed from these factors are 5, 17, and 23. Therefore, the three prime numbers less than 30 whose product is 1955 are 5, 17, and 23.

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!

Well, darling, the prime numbers that add up to 92 are 89 and 3. 89 is a prime number because it's only divisible by 1 and itself, and 3 is also a prime number for the same reason. So, when you add those two bad boys together, you get 92. Voila!

Here are the first 33 prime numbers. I don't have time to multiply them. Perhaps you do.

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137

Oh, dude, the square number between 10 and 20 is 16. It's like 4 squared, you know, 4 times 4. So, if you're ever in a situation where someone asks you for the square number between 10 and 20, you can confidently say 16 and impress absolutely no one.

The smallest prime number greater than 30 is 31. A prime number is a number greater than 1 that can only be divided by itself and 1 without leaving a remainder. In this case, 31 is indivisible by any other number besides 1 and itself, making it the smallest prime number greater than 30.

The only prime number with two digits whose digits sum to 14 is 59. To determine this, we can list out the prime numbers with two digits (from 10 to 99) and check which one has digits that sum up to 14. The only number that satisfies this condition and is also a prime number is 59.

The prime numbers between 4 and 12 are 5 and 7. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In this case, 5 and 7 are the only prime numbers within the given range, as 4, 6, 8, 9, 10, and 12 are all composite numbers.

31,37 are not composite

In the more widely used American system, 1 with 48 zeroes is called a quindecillion or quinquadecillion. In the traditional British system and in continental Europe, 1 with 48 zeroes is called an octillion.

3 composite numbers, 21, 22, and 24, are greater than 20 but less than 25.

To determine if the ages of relatives of 6 are prime or composite numbers, we need to consider the factors of each age. A prime number is a number greater than 1 that has only two factors: 1 and itself. If the age is divisible by any number other than 1 and itself, it is a composite number. For example, if a relative is 7 years old, it is a prime number as it has only two factors: 1 and 7. Conversely, if a relative is 8 years old, it is a composite number as it has factors other than 1 and 8 (2 and 4).

Well, honey, it's simple math. Prime numbers are only divisible by 1 and themselves. If you can divide a number by anything other than 1 and itself, it ain't prime. So, if you try dividing 32 by 2, 4, 8, or 16, and 95 by 5 or 19, you'll see they ain't prime, sweetie.

900 = 9 x 100 = 3 x 3 x 4 x 25 = 3 x 3 x 2 x 2 x 5 x 5 = 22 x 32 x 52

The multiples of 9 are numbers that can be divided evenly by 9. The two prime numbers closest to a multiple of 9 are 7 and 11. Since 9 is between 7 and 11, the multiple of 9 that is in between these two prime numbers is 9 itself.

To determine the number of times the digit 1 appears between 1 and 120, we can consider each place value separately. In the units place, the digit 1 appears 12 times (1, 11, 21, ..., 111). In the tens place, the digit 1 appears 11 times (10, 11, 12, ..., 19). Therefore, the total number of times the digit 1 appears between 1 and 120 is 12 (from the units place) + 11 (from the tens place) = 23 times.

To find a number less than 100 that is divisible by 2, 5, and 9, we need to find the least common multiple (LCM) of these three numbers. The LCM of 2, 5, and 9 is 90. Therefore, the number less than 100 that is divisible by 2, 5, and 9 is 90.

The only prime between 8 and 12 is 11.

To find out if a number is prime, just try dividing it by all prime numbers between 2 and that number (including 2). The easiest method to do this is to write all numbers from 2 to your number down. Then cross out all numbers divisible by 2. Now cross out all numbers divisible by the next lowest number that is not crossed out (which is 3). Repeat this last step (the next number should be 5, then 7, then 11) until you reach your number, or you cross it out. If you have crossed it out, it is not a prime number, and if it has not been crossed out it is a prime number.