Factoring and Multiples

A common factor of 32, 64, and 76 is a number that divides evenly into all three of these numbers. To find the common factors, we can first find the prime factorization of each number. The prime factorization of 32 is 2^5, the prime factorization of 64 is 2^6, and the prime factorization of 76 is 2^2 * 19. The common factor among these three numbers is 2^2, which is 4.

Prime factorization is the finding which prime number multiply to get to make the original number.

Factors of 75: 1, 3, 5, 15, 25, 75

Prime factors: 3, 5

3 x 5 x 5 = 75

Ah, the Highest Common Factor, isn't that a happy little concept? Let's see, to find the HCF of 260, we can break it down into its prime factors, which are 2 x 2 x 5 x 13. Then, we look for the common factors it shares with other numbers to find the highest one. Remember, there are no mistakes, just happy little accidents in mathematics!

The multiples of 0.24 are numbers that can be obtained by multiplying 0.24 by any integer. In other words, the multiples of 0.24 are 0.24, 0.48, 0.72, 0.96, and so on. These multiples form a sequence that increases by 0.24 each time.

To factor the expression 3x^2 - 9x^3, we first need to find the greatest common factor (GCF) of the two terms. The GCF of 3x^2 and 9x^3 is 3x^2. We can factor out 3x^2 from both terms to get 3x^2(1 - 3x). Therefore, the factored form of 3x^2 - 9x^3 is 3x^2(1 - 3x).

A prime factorization is the process of breaking down a composite number into its prime factors, which are numbers that are only divisible by 1 and themselves. This is typically done by dividing the number by the smallest prime number possible and continuing to divide the quotients by prime numbers until only prime numbers remain. The prime factorization of a number is unique, and it can be represented as a product of prime numbers. For example, the prime factorization of the number 24 is 2 x 2 x 2 x 3, or 2^3 x 3.

Well, honey, the greatest common factor of 24, 45, and 48 is 3. It's like finding the one thing all three of them have in common - in this case, it's 3. So, there you have it, 3 is the magic number that can divide all those numbers without leaving a remainder.

The highest common factor (HCF) of 56 and 160 is the largest number that divides both 56 and 160 without leaving a remainder. To find the HCF, we need to determine the common factors of 56 and 160, which are 1, 2, 4, and 8. The highest common factor of 56 and 160 is 8.

The Highest Common Factor (HCF) of 18 and 30 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, we need to determine the common factors of 18 (1, 2, 3, 6, 9, 18) and 30 (1, 2, 3, 5, 6, 10, 15, 30) and identify the largest one they share, which is 6. Therefore, the HCF of 18 and 30 is 6.

The multiples of 11 are numbers that can be divided evenly by 11. To find the multiples of 11 up to 2000, we can start by finding the first multiple of 11, which is 11 itself. The next multiples would be 22, 33, 44, and so on. Continuing this pattern, we find that the multiples of 11 up to 2000 are 11, 22, 33, 44, ..., 1988, 1999.

To find two numbers that multiply to -317, we need to consider the factors of -317. The factors of 317 are 1, 11, 29, and 317. Since -317 is negative, the two numbers must have different signs. Therefore, the pair of numbers that multiply to -317 is -1 and 317.

Oh, dude, you want me to do math now? Like, fine, but only because I'm feeling generous today. So, if we're talking about what times what equals 172, it's like 2 times 86, or 4 times 43. You're welcome for that mind-blowing revelation.

Alright, buckle up buttercup. The factors of 258 are 1, 2, 3, 6, 43, 86, 129, and 258. And for 344, we've got 1, 2, 4, 8, 43, 86, 172, and 344. So there you have it, the cold hard truth about the factors of 258 and 344.

To find the greatest common factor (GCF) of 56, 84, and 140, we first need to factor each number. The prime factorization of 56 is 2^3 * 7, 84 is 2^2 * 3 * 7, and 140 is 2^2 * 5 * 7. To find the GCF, we look for the highest power of each prime factor that appears in all three factorizations, which in this case is 2^2 * 7, resulting in a GCF of 28.

Oh, what a delightful question we have here! To find out what times what equals 1764, we can break it down into factors. 1764 can be expressed as 42 multiplied by 42. Isn't that just a happy little fact to discover?

Oh, dude, the Highest Common Factor (HCF) of 6 and 30 is like the biggest number that can divide both of them without leaving a remainder. So, you look at the factors of 6 (1, 2, 3, 6) and 30 (1, 2, 3, 5, 6, 10, 15, 30) and find the biggest one they have in common. In this case, it's 6. So, the HCF of 6 and 30 is 6. Easy peasy, lemon squeezy!

To find the average of a set of numbers, you add all the numbers together and then divide by the total count of numbers. In this case, the sum of the numbers 2.65, 2.75, 2.80, 2.77, 2.60, 2.65, and 2.68 is 18.90. Since there are 7 numbers in the set, the average would be 18.90 divided by 7, which equals approximately 2.70.

Well, honey, the factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, and 690. As for prime factorization, you can break it down into 2 x 3 x 5 x 23. Hope that clears things up for ya!

The common factors for 39 and 52 are the numbers that can evenly divide both 39 and 52 without leaving a remainder. The common factors of 39 are 1, 3, 13, and 39, while the common factors of 52 are 1, 2, 4, 13, 26, and 52. Therefore, the only common factor for both 39 and 52 is 13.

They involve the same relationship. The major difference is grammatical. "Multiple" is a noun, meaning a number that can be divided by another number without a remainder.

"Divisible" is an adjective, meaning capable of being divided by another number without a remainder.

12 is a multiple of 3. In this sentence, the word "multiple" refers to the number 12.

12 is divisible by 3. In this sentence, "divisible" refers to a quality that 12 has.

The highest common factor (HCF) of 40 and 72 is the largest number that divides both 40 and 72 without leaving a remainder. To find the HCF, we need to identify the common factors of 40 and 72, which are 1, 2, 4, and 8. The highest common factor of 40 and 72 is 8.

The GCF of 32, 48, and 64 is 16.

Oh, dude, the Highest Common Factor (HCF) of 55, 132, and 143 is 11. It's like the cool kid that can divide all these numbers without leaving any remainders. So yeah, 11 is the HCF, no big deal.

Oh, what a happy little question! Well, if we're looking for numbers that can go into 431, we can start by thinking about factors like 1, 7, 61, and 431 itself. Each of these numbers can be multiplied to fit perfectly into 431, just like adding different colors to create a beautiful painting. Remember, there's no mistakes here, just happy little numbers waiting to be discovered.

To find the Greatest Common Factor (GCF) of 27, 63, and 81, we first need to find the prime factors of each number. The prime factorization of 27 is 3 x 3 x 3, the prime factorization of 63 is 3 x 3 x 7, and the prime factorization of 81 is 3 x 3 x 3 x 3. The GCF is the product of the common prime factors raised to the lowest power they appear in any of the numbers, which in this case is 3 x 3 x 3 = 27. Therefore, the GCF of 27, 63, and 81 is 27.