Factoring and Multiples

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.

Numbers that have 2 as a factor are those that are divisible by 2 without leaving a remainder. This includes all even numbers such as 2, 4, 6, 8, 10, and so on. In other words, any number that can be expressed as 2 multiplied by another integer is a number that has 2 as a factor.

Oh, dude, the positive difference between the number of distinct prime factors of 15 squared (225) and 64 cubed (262,144) is like 4. Prime factors are like those VIP numbers that can't be divided by anything except 1 and themselves. So, 225 has 2 distinct prime factors (3 and 5), and 262,144 has 1 distinct prime factor (2). Subtract 1 from 2, and you get 1. Wow, math can be fun, right?

Numbers that are divisible by 1024 are multiples of 1024, meaning they can be expressed as 1024 times an integer. In other words, any number that can be written as 1024 x n, where n is an integer, is divisible by 1024. Some examples of numbers divisible by 1024 are 1024, 2048, 3072, and so on.

The prime factors of 180 are the prime numbers that can be multiplied together to equal 180. To find the prime factors of 180, we start by dividing 180 by the smallest prime number, which is 2. Continuing this process, we find that the prime factors of 180 are 2, 2, 3, 3, and 5, represented as 2^2 * 3^2 * 5.

Oh, dude, multiples of 4 are like 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, and so on. So, if you're looking for multiples of 4 that are not 48, just ignore 48 on that list. It's like a party where everyone's invited except for 48.

Well, honey, the common multiples of 6, 8, and 12 are numbers that can be divided by all three without leaving a pesky remainder. So, grab your calculator and start multiplying those numbers until you find the ones that satisfy all three divas. Good luck, darling!

21

The highest common factor (HCF) of 22 and 58 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, you can use methods like prime factorization or the Euclidean algorithm. In this case, the prime factorization of 22 is 2 x 11 and the prime factorization of 58 is 2 x 29. The common factor between them is 2, so the HCF of 22 and 58 is 2.

Oh, dude, the Highest Common Factor (HCF) of 490 and 1050 is 70. It's like the cool kid that hangs out with both 490 and 1050 without any drama. So, yeah, 70 is the number that divides both 490 and 1050 without leaving any remainder.

Ah, the least common multiple is like finding a happy little spot where both numbers can come together peacefully. To find it, you look for the smallest number that both 270 and 360 can both be divided into evenly. So, the least common multiple of 270 and 360 is 1080. Just imagine those numbers dancing together in perfect harmony!

Oh, dude, the greatest common factor of 36, 60, and 108 is 12. It's like the cool kid at the math party that all these numbers can hang out with. So yeah, 12 is their BFF, keeping things simple and dividing them all with no drama.

Well, honey, the LCM of 6a and 8a is 24a. You see, you just gotta find the smallest number that both 6 and 8 can divide into evenly, and then slap on that 'a' like it's nobody's business. So, there you have it, 24a is the name of the game.