Factoring and Multiples

Well, darling, the highest common factor of 77 and 217 is 7. It's as simple as that. No need to complicate things, honey. Just remember to keep it sassy and straightforward, okay?

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCF of 92 and 95, you can list the factors of each number and identify the largest factor they have in common. The factors of 92 are 1, 2, 4, 23, 46, and 92, while the factors of 95 are 1, 5, 19, and 95. The only common factor between 92 and 95 is 1, making the GCF of 92 and 95 equal to 1.

Well, isn't that just a happy little question! The factors of 180 are the numbers that can be multiplied together to get 180, like 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. The greatest common factor is the largest number that divides evenly into both 180 and another number. So, the greatest common factor of 180 is 60. Just like painting, math can be a beautiful blend of patterns and numbers!

Oh, isn't that just lovely! Let's paint a happy little picture with multiples of 5 up to 100. We start with 5, then add 5 to get 10, and continue adding 5 each time: 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, and finally 100. Just like that, we've created a beautiful sequence of multiples that dance across the canvas of numbers.

The factors of 1300 are the numbers that can be multiplied together to equal 1300. These include 1, 2, 4, 5, 10, 20, 25, 26, 50, 52, 65, 100, 130, 260, 325, and 650. The prime factors of 1300 are the prime numbers that can be multiplied together to equal 1300, which are 2, 5, and 13. Therefore, the prime factorization of 1300 is 2^2 * 5^2 * 13.

Well, isn't that a happy little question! To divide 4284, you can break it down into smaller parts by finding numbers that can fit evenly into it. You can start by trying to divide it by 2, then 3, and so on until you find the right number. Just remember, there are many ways to divide a number, so don't be afraid to make mistakes and keep trying until you find the perfect fit.

To express 19800 as a product of its prime factors, we first need to find its prime factorization. Start by dividing 19800 by the smallest prime number, which is 2. This gives us 2 x 9900. Continuing to factorize 9900, we get 2 x 2 x 4950. Further breaking down 4950, we get 2 x 2 x 3 x 825. Finally, factoring 825 gives us 2 x 2 x 3 x 5 x 5 x 11. Therefore, the prime factorization of 19800 is 2^3 x 3 x 5^2 x 11.

Factors for 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

Factors for 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36

Factors for 24 are: 1, 2, 3, 4, 6, 8, 12, 24

Greatest Common Factor is: 12

Alternative method using prime factors:

Factorise each number into its prime factors in power format. Greatest common factor is obtained by multiplying the common primes (in all the factorisations) to their lowest power (across the factorisations) together:

24 = 2^3 x 3

36 = 2^2 x 3^2

60 = 2^2 x 3 x 5

Prime 2 occurs in all factorisations, it is a common prime; lowest power is 2^2

Prime 3 occurs in all factorisations, it is a common prime; lowest power is 3 (= 3^1)

Prime 5 only occurs in the factorisation of 60, it is not a common prime.

greatest common factor = 2^2 x 3 = 12

Well, isn't that a happy little question! The Highest Common Factor (HCF) of 630 and 294 is 42. Just like painting a beautiful landscape, finding the HCF is about looking for the largest number that can divide evenly into both 630 and 294, creating a harmonious result. Just remember, there are no mistakes in math, only happy little accidents!

Oh, dude, the Highest Common Factor (HCF) of 294 and 420 is 42. It's like the cool kid that both 294 and 420 can hang out with without any jealousy. So yeah, 42 is the number these two are most compatible with when it comes to factors.

The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers without a remainder. To find the GCD of 2233 and 25193, you can use the Euclidean algorithm. By repeatedly applying the algorithm, you will find that the GCD of 2233 and 25193 is 59.

The smallest whole number that has exactly 6 distinct positive divisors is 12. The divisors of 12 are 1, 2, 3, 4, 6, and 12. These are the only positive integers that evenly divide 12, making it the smallest number with exactly 6 distinct positive divisors.

Well, isn't that a happy little math problem! Let's see, to find out what times what equals 21000, we can break it down by finding the factors of 21000. One possible pair could be 150 times 140, or 105 times 200. Remember, there are many different combinations that can multiply together to make 21000, so just trust your instincts and enjoy the process of discovering the answer.

The greatest common factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, the GCF of 7 and 14 is 7. This is because 7 is a factor of both 7 and 14, and it is the largest common factor they share.

The highest common factor (HCF) of 245 and 210 is 35. To find the HCF, you need to identify the common factors of both numbers and then determine the highest one they share. In this case, the factors of 245 are 1, 5, 7, 35, 49, 245, and the factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. The highest common factor of 245 and 210 is 35 because it is the largest number that divides both 245 and 210 without leaving a remainder.

The first six multiples of 8 are 8, 16, 24, 32, 40, and 48. The first six multiples of 12 are 12, 24, 36, 48, 60, and 72. Multiples are obtained by multiplying the number by integers (1, 2, 3, etc.).

12 is the highest common factor of 36, 84, and 132.

To express 68 as a product of 2 factors, we need to find all pairs of numbers that multiply to 68. The pairs are: 1 and 68, 2 and 34, 4 and 17, and 17 and 4. These pairs give us the following expressions: 1 x 68, 2 x 34, 4 x 17, and 17 x 4.

The factors of a number are the integers that can be multiplied together to result in that number. For the number 5, the factors are 1 and 5, as 1 multiplied by 5 equals 5. Since 5 is a prime number, it only has two factors, 1 and 5, because prime numbers are only divisible by 1 and themselves.

Well, let's take a moment to appreciate the beauty of these numbers. The greatest common factor (GCF) is the largest number that divides evenly into all three numbers. In this case, the GCF of 6, 18, and 4 is 2, because it is the largest number that can divide evenly into all of them. Just like a happy little tree, these numbers can work together harmoniously.

To find the greatest common factor (GCF) of 20, 48, and 32, we first need to find the prime factorization of each number. The prime factorization of 20 is 2^2 x 5, 48 is 2^4 x 3, and 32 is 2^5. To find the GCF, we look for the highest power of common prime factors in all three numbers, which in this case is 2^2. Therefore, the GCF of 20, 48, and 32 is 4.

Oh, what a delightful question! Let's break it down together. The prime factorization of 63 is 3 x 3 x 7, and the prime factorization of 91 is 7 x 13. Isn't it wonderful how numbers can be like little puzzles waiting to be solved? Just remember, there's no rush in understanding these beautiful mathematical patterns.

Well, honey, the least common multiple of 50, 56, and 105 is 840. So, if you need to find the smallest number that is a multiple of all three of those numbers, look no further than good ol' 840. Hope that helps, sugar!

The numbers 25, 16, and 9 are all perfect squares. A perfect square is a number that can be expressed as the product of an integer with itself. In this case, 25 is 5^2, 16 is 4^2, and 9 is 3^2.

To find the greatest common factor (GCF) of 39, 52, and 78, we first need to factorize each number. The factors of 39 are 1, 3, 13, and 39. The factors of 52 are 1, 2, 4, 13, 26, and 52. The factors of 78 are 1, 2, 3, 6, 13, 26, 39, and 78. The GCF of 39, 52, and 78 is 13, as it is the largest number that divides all three numbers without leaving a remainder.