Factoring and Multiples

When finding the GCF of a set of numbers, firstly express each number as a product of its prime factors.

28 = 2 x 2 x 7

42 = 2 x 3 x 7

56 = 2 x 2 x 2 x 7

The factors that each number has in common are 2 and 7.

The Greatest Common Factor is therefore 2 x 7 = 14

The greatest common factor (GCF) of 21 and 306 is 3. To find the GCF, you need to identify the factors of each number. The factors of 21 are 1, 3, 7, and 21, while the factors of 306 are 1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 153, and 306. The largest number that both 21 and 306 share as a factor is 3, making it the greatest common factor.

To simplify 75 over 300, we first find the greatest common factor of both numbers, which is 75. Dividing both numbers by 75 gives us 1 over 4. Therefore, 75 over 300 simplifies to 1 over 4.

Oh, dude, it's like this - so, 1.25 is the same as 125%, right? And if you want to convert that to 25%, you just move the decimal point two places to the left, which makes it 0.25. So technically, 1.25 equals 125%, but if you want to be all specific and convert it to 25%, you gotta shift that decimal around a bit.

The even multiples of pi are numbers that can be expressed as 2nπ, where n is an integer. This means that the even multiples of pi are any number that is a multiple of pi and also an even number. Examples of even multiples of pi include 0, 2π, 4π, -2π, -4π, etc.

Oh, dude, you want me to list all the factors of 35? Like, seriously? Alright, brace yourself - you've got 1, 5, 7, and 35. That's it. Like, there you go, all the factors of 35 in a neat little package. You're welcome.

The common factors of 270 and 3000 are numbers that can evenly divide both 270 and 3000 without leaving a remainder. To find the common factors, we first need to find the prime factorization of each number. The prime factorization of 270 is 2 x 3^3 x 5, and the prime factorization of 3000 is 2^3 x 3 x 5^3. By comparing the prime factors of both numbers, we can identify the common factors as 2, 3, and 5.

Well, isn't that a happy little question! To find the sum of the first 6 multiples of 9, you simply add them all together. So, 9 + 18 + 27 + 36 + 45 + 54 equals 189. Just like painting a beautiful landscape, math can be a peaceful and rewarding experience.

35

Well, honey, the number you're looking for is 6. It's a factor because you can divide 6 by 1, 2, 3, and 6 without any remainder, and it's a multiple because you can multiply 6 by 1, 2, 3, and so on to get multiples of 6. So, there you have it, 6 is the lucky winner in this scenario.

To find the greatest common factor (GCF) of 126 and 420, we first need to list the factors of each number. The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126. The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, and 420. The GCF of 126 and 420 is 42, as it is the greatest factor that both numbers share.

Well, darling, the greatest common factor of 280 and 320 is 40. It's like finding the perfect pair of shoes that both numbers can comfortably strut their stuff in. So, there you have it, the sassy math queen has spoken!

The greatest common factor (GCF) is often also called the greatest common divisor (GCD) or highest common factor (HCF). Keep in mind that these different terms all refer to the same thing: the largest integer which evenly divides two or more numbers.

The greatest common factor of 36 and 216 is 36

Oh, dude, totally! So, like, the positive factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. You can pair them up as follows: (1, 36), (2, 18), (3, 12), and (4, 9). So, yeah, you can totally pair up all the positive factors of 36.

Well, isn't that just a happy little question! The factor rainbow of the number 99 is a beautiful array of colors representing its factors. We start with the number 1 and 99, then move on to 3 and 33, and finally, 9 and 11. Just imagine each factor as a different color blending together to create a lovely rainbow of numbers.

The GCF is 8.

The greatest common factor (GCF) is often also called the greatest common divisor (GCD) or highest common factor (HCF). Keep in mind that these different terms all refer to the same thing: the largest integer which evenly divides two or more numbers.

The greatest common factor of 30, 60, 75, and 90 is 15.

Oh, isn't that a happy little question? Let's take a look at those numbers. The common factors of 102 and 204 are 1, 2, 3, 6, 17, 34, 51, and 102. Just like painting a beautiful landscape, finding common factors is all about seeing the connections between numbers and appreciating the harmony they create.

Well, honey, the greatest common factor of 16, 40, and 88 is 8. It's like finding the biggest slice of cake that all three numbers can share without any leftovers. So, grab a fork and enjoy that sweet math treat!

To find the highest common factor of 55, 77, and 143, you need to determine the factors of each number. The factors of 55 are 1, 5, 11, and 55. The factors of 77 are 1, 7, 11, and 77. The factors of 143 are 1, 11, 13, and 143. The highest common factor among the three numbers is 11, as it is the largest factor that they all share.

They both read the same when rotated 180 degrees.

Oh, what a happy little question! Let's see here... the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Now, the square numbers among these factors are 1, 4, and 9. Isn't it wonderful how numbers can come together like this? Just like painting a beautiful picture!

To simplify the number 830, we need to find the greatest common factor (GCF) between 830 and any other number. In this case, the number 830 is already in its simplest form because it cannot be divided evenly by any other number except 1 and itself. Therefore, 830 in simplest form remains as 830.

No, 2x2x2x3x5x5 is not a prime factorization. A prime factorization is a representation of a number as a product of prime numbers. In this case, 2x2x2x3x5x5 can be simplified to 2^3 x 3 x 5^2, which is the prime factorization of the number.

The GCF is 30.