Factoring and Multiples

63

Well, honey, the greatest common factor of 64, 96, and 128 is 32. It's like finding the one friend who shows up to every party - dependable and always there when you need them. So, go ahead and thank good ol' 32 for being the life of the math party.

Well, darling, the greatest common factor (GCF) of 14, 2, and 21 is 1. Why? Because there ain't no other number that can divide all three of those numbers evenly. So, there you have it, the sassy truth!

Well, isn't that just a happy little question! If we take 100 and divide it by .05, we find that it goes in 2000 times. Just imagine all those little divisions coming together to create a beautiful painting of numbers. Remember, there are no mistakes, just happy little accidents in math!

To find the common factors of 18 and 54, we first need to determine the factors of each number. The factors of 18 are 1, 2, 3, 6, 9, and 18, while the factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The common factors of 18 and 54 are 1, 2, 3, 6, 9, and 18. In a Venn diagram, we can represent the factors of 18 in one circle and the factors of 54 in another, with the overlapping region containing the common factors.

The product of 24.6 and 1.2 is 29.52, which is calculated by multiplying the two numbers together. The quotient of 24.6 divided by 1.2 is 20.5, which is obtained by dividing the first number by the second. These calculations are fundamental operations in arithmetic and can be easily computed using a calculator or by hand.

Oh, dude, it's like 9 times 10. I mean, you could also do 45 times 2, but who's got time for that? So yeah, 9 times 10, easy peasy lemon squeezy.

41.66666667 as a fraction is best represented as 41 and 2/3. To convert the decimal to a fraction, we first note that the decimal portion .66666667 can be expressed as a repeating decimal, which is equivalent to 2/3. Therefore, 41.66666667 is equal to 41 + 2/3, or 41 2/3 in mixed number form.

Well, isn't that a happy little math question! The Highest Common Factor (HCF) of 112 and 168 is 56. You see, just like painting, math is all about finding the beauty in numbers and patterns. Happy calculating, my friend!

True. Even numbers are even because they are multiples of 2. That means that any two even numbers will have at least 2 as a common factor. Since that number (the GCF) will have 2 as a factor, it will be a multiple of 2: an even number.

Oh, dude, the greatest common factor of 14, 35, and 84 is 7. It's like the number that can divide all three of those numbers without leaving any remainder. So, yeah, 7 is the cool kid that all these numbers can hang out with without any drama.

Well, isn't that a happy little math problem we have here? To find the greatest common factor of 324m and 7m, we look for the largest number that can divide both 324 and 7 evenly. In this case, the greatest common factor is just m, because it's the largest factor that both terms share. Just remember, there are no mistakes in math, only happy little accidents!

Oh, what a happy little question we have here! The common factor of 20x4 and 6x3 is 2x3. Just like painting a beautiful landscape, finding common factors is all about looking for the elements that both numbers share. Keep up the good work, my friend!

Prime factor each number. Circle the factors that are in all three numbers. Multiply those factors.

27=3x3x3

54=2x3x3

72=2x2x2x3x3

3x3=9 is the GCF

To get the number 16 using only the digits 1, 2, 3, and 4, you can use the following mathematical expression: (4 x 3) + (2 x 1) = 12 + 4 = 16. This equation involves multiplication and addition, using each of the given digits exactly once.

To find a number that can be divided by both 63 and 10, we need to find the least common multiple (LCM) of the two numbers. The LCM of 63 and 10 is 630. Therefore, any number that is a multiple of 630 can be divided by both 63 and 10.

The factors of 32 are 1, 2, 4, 8, 16, and 32. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Factors are numbers that can be multiplied together to get the original number.

The common multiples of 3, 4, and 8 are numbers that are divisible by all three of these numbers. To find the common multiples, we first list the multiples of each number:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 8: 8, 16, 24, 32, ...
The common multiples of 3, 4, and 8 are 24, 48, and so on, as they are the numbers that appear in the lists of multiples of all three numbers.

Well, honey, the number with the prime factorization of 2x2x3x5 is 60. It's like a math puzzle, but not really. Just multiply those primes together and you've got your answer. Math can be fun...or at least tolerable.

It is: 10 that is the HCF of 30, 210 and 700

To find the least common multiple (LCM) of 18 and 24, we first need to find the prime factorization of each number. The prime factorization of 18 is 2 x 3^2 and the prime factorization of 24 is 2^3 x 3. To find the LCM, we take the highest power of each prime factor that appears in either factorization, which gives us 2^3 x 3^2 = 72. Therefore, the least common multiple of 18 and 24 is 72.

The three factors to consider in harvesting are timing, technique, and equipment. Timing refers to choosing the right moment to harvest to ensure optimal quality and yield. Technique involves the methods used to harvest, such as hand-picking or machine harvesting, depending on the crop. Equipment selection is crucial to ensure efficiency and minimize damage to the crop during harvesting operations.

Let's denote the two numbers as x and y. From the given conditions, we have the following system of equations:

x + y = 9 xy = 168

By solving the first equation for y (y = 9 - x) and substituting it into the second equation, we get:

x(9 - x) = 168 9x - x^2 = 168 x^2 - 9x + 168 = 0

Factoring the quadratic equation gives us (x - 8)(x - 21) = 0. Therefore, the two numbers are 8 and 21.

Oh, dude, like, yeah, totally! 8 can totally go into 85. You can fit 10 eights into 85, with a remainder of 5. So, technically, 8 does go into 85. Math can be fun, right?