Factoring and Multiples

To find the common factors of 123 and 555, we first need to determine the factors of each number. The factors of 123 are 1, 3, 41, and 123. The factors of 555 are 1, 3, 5, 15, 37, 111, and 555. The common factors of 123 and 555 are 1 and 3. Therefore, they have 2 common factors.

Oh, dude, 9 over 10 in simplest form is like, well, 9 over 10. That's already as simple as it gets. It's not like we can simplify it further without changing the value. So yeah, 9 over 10 is the simplest form of 9 over 10.

The prime factorization of 32 is 2^5, where 2 is the prime factor and 5 is the exponent. This means that 32 can be expressed as 2 multiplied by itself 5 times. In exponential form, this is written as 2^5.

The number 29 is a prime number, which means it only has two factors: 1 and 29. Prime numbers are numbers that are divisible only by 1 and themselves. In the case of 29, it cannot be divided evenly by any other numbers.

Well, darling, 380 can be equal to a lot of things depending on the context. It could be the sum of 190 and 190, the product of 38 and 10, or the result of subtracting 20 from 400. So, the possibilities are endless, just like my wit.

The Highest Common Factor (HCF) of 64 and 56 is 8. To find the HCF, you can determine the factors of both numbers: 64 (1, 2, 4, 8, 16, 32, 64) and 56 (1, 2, 4, 7, 8, 14, 28, 56). The largest number that appears in both lists is 8, making it the HCF of 64 and 56.

Well, isn't that a happy little math question! Let's see, to find two numbers that multiply together to make 192, we can think of different combinations like 12 and 16, or 8 and 24. Just remember, there are many possibilities, so don't be afraid to explore and find the right pair that fits perfectly like a brushstroke on a canvas. Happy calculating, my friend!

Oh, dude, you're hitting me with the math questions, huh? So, a number that's a factor of 1000 but not 10000 and is a multiple of both 50 and 8... Well, 40 fits the bill. It divides into 1000, but not into 10000, and it's the product of 50 and 8. Math can be fun, right?

A composite number is a positive integer greater than 1 that has more than two distinct positive divisors. In this case, 63 is a composite number because it can be divided evenly by 1, 3, 7, 9, 21, and 63. The other numbers listed (13, 61, and 31) are all prime numbers because they only have two distinct positive divisors, 1 and the number itself.

20

The greatest common factor (GCF) of two numbers is the largest number that divides evenly into both numbers. In this case, the factors of 55 are 1, 5, 11, and 55. The factors of 5 are 1 and 5. The greatest common factor of 55 and 5 is 5, as it is the largest number that divides evenly into both 55 and 5.

132 = 2 x 2 x 3 x 11 = 22 x 3 x 11

Oh, dude, the LCM of 14 and 46 is 322. It's like the smallest number that both 14 and 46 can divide into evenly without leaving a remainder. So, yeah, 322 is the winner here.

Well, darling, 13 times 17 equals 221. So there you have it, simple math for a simple question. Hope that clears things up for you!

(5 x 8) + (2 x 8) = 7 x 8 = 56

Well, isn't that just a happy little question! You see, 135 can be divided by different numbers like 1, 3, 5, 9, 15, 27, 45, and 135 itself. It's like a beautiful landscape with many possibilities, all waiting to be explored and appreciated. Just remember, there are no mistakes, only happy accidents in the world of numbers.

The factors of 181 are 1 and 181, as 181 is a prime number. Prime numbers are numbers that are only divisible by 1 and themselves. In this case, since 181 is only divisible by 1 and 181, those are the only factors of 181.

Oh, isn't finding the greatest common factor like finding a happy little tree in a beautiful forest? The greatest common factor of 15, 20, and 35 is 5. Just like how a painter mixes colors to create harmony on the canvas, we find the factors they all share to create harmony in our math problem. Just remember, there are no mistakes, just happy little accidents in math!

Oh, dude, the whole number with the greatest prime factor between 1 and 30 is 30 itself. The greatest prime factor of 30 is 5, which is the largest prime number between 1 and 30. So, yeah, 30 takes the crown for this one.

The multiples of 8 are numbers that can be divided evenly by 8. To find the multiples of 8 up to 500, we can start by listing the multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496.

To factor the expression 21x^35, you need to find the common factors of 21 and x^35. The factors of 21 are 1, 3, 7, and 21. The factors of x^35 are x, x^2, x^3, ..., x^35. Therefore, the factored form of 21x^35 is 21x*x^34 or 21x^(35-1).

Alright, sweetheart, buckle up. The greatest common factor of 12, 18, and 36 is 6. It's like finding the perfect little black dress that fits all three of them without any alterations. So, there you have it, 6 is the MVP in this mathematical fashion show.

Well, let's think about this like a happy little math problem. The highest common factor, or HCF, of 12, 20, and 36 is the largest number that divides evenly into all three of them. So, if we look at the factors of each number, we see that the HCF of 12, 20, and 36 is 4. Just like painting a beautiful landscape, finding the HCF is all about finding the common elements that bring everything together in harmony.

Well, darling, the factors of 2368 are 1, 2, 4, 8, 16, 148, 296, 592, and 2368 itself. So, if you were hoping for some fancy math magic, sorry to disappoint, but those are the cold, hard facts.

To find the Least Common Multiple (LCM) of 4, 3, 7, and 5, we first need to prime factorize each number. The prime factors of 4 are 2^2, 3 is a prime number itself, 7 is a prime number, and 5 is also a prime number. The LCM is then calculated by taking the highest power of each prime factor that appears in any of the numbers, which results in 2^2 * 3 * 5 * 7 = 420. Therefore, the LCM of 4, 3, 7, and 5 is 420.