Factoring and Multiples

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.

Oh, dude, the LCM of 32 and 15 is like the smallest number that both 32 and 15 can divide evenly into. So, you take the prime factors of each number, which are 2^5 and 3 * 5, then you just multiply the highest power of each prime factor together. That gives you 2^5 * 3 * 5, which equals 480. So, the LCM of 32 and 15 is 480.

To find the Greatest Common Factor (GCF) of 35, 65, and 90, we need to first find the prime factorization of each number.

35 = 5 x 7 65 = 5 x 13 90 = 2 x 3 x 3 x 5

Next, we identify the common prime factors among the numbers, which are 5. Therefore, the GCF of 35, 65, and 90 is 5.

The number eight is divisible by 1, 2, 4, and 8. This is because 8 divided by 1 equals 8, 8 divided by 2 equals 4, 8 divided by 4 equals 2, and 8 divided by 8 equals 1. These are the numbers that evenly divide into eight without leaving a remainder.

The prime factorization of 25n^2 is 5 * 5 * n * n, or simply 5^2 * n^2. This means that the prime factors of 25n^2 are 5 and n, each raised to the power of 2. In other words, 25n^2 can be expressed as the product of 5 squared and n squared.

When something increases by a factor of 16, it means that the quantity has been multiplied by 16. For example, if you have a value of 5 and it increases by a factor of 16, the new value would be 5 x 16 = 80. This is a significant increase compared to just adding 16 to the original value.

Oh, what a happy little question! Let's see here... multiples of 4 less than 100 are numbers that you get when you multiply 4 by another number and the result is less than 100. So, we have 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, and 96. Just like painting, finding multiples can be a fun and calming experience.

Oh, isn't that just a happy little question! Let's take a moment to appreciate the factors of 15 and 65. The common factors of 15 and 65 are 1 and 5, as they can both divide evenly into both numbers. It's like a little math puzzle waiting to be solved, and you're doing great just by asking!

To find 1/8 of 88, you would divide 88 by 8. This calculation results in 11, so 1/8 of 88 is 11. This can be verified by multiplying 11 by 8, which equals 88.

Well, honey, the highest common factor (HCF) of 9, 54, and 18 is 9. You see, 9 is the largest number that can divide all three numbers without leaving a remainder. So, there you have it - the sassy math answer you didn't know you needed.

To find the Greatest Common Factor (GCF) of 45 and 65, we first need to list the factors of each number. The factors of 45 are 1, 3, 5, 9, 15, and 45, while the factors of 65 are 1, 5, 13, and 65. The largest number that appears in both lists is 5, so the GCF of 45 and 65 is 5.

The highest common factor of 875 is 125. To find the highest common factor, you need to identify all the factors of the number and then determine the largest factor that is common to all of them. In this case, the factors of 875 are 1, 5, 25, 35, 125, and 875. The highest common factor among these factors is 125.

Oh, what a happy little question! Let's take a moment to appreciate the factors of 144. You see, 144 can be divided evenly by 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. It's like a beautiful symphony of numbers coming together to create harmony on our canvas of mathematics.

Oh honey, 84 is just begging to be broken down. In exponential form, you've got 2^2 * 3^1 * 7^1. It's like a math party, and 84 is the guest of honor!

Oh, dude, the greatest common factor of 120 and 600 is 120. It's like the biggest number that can divide both of them without leaving a remainder. So yeah, 120 is the winner here.

To determine what number 4, 5, 6, and 8 can all go into, we need to find the highest common factor of these numbers. The highest common factor of 4, 5, 6, and 8 is 1 because these numbers do not share any factors other than 1. Therefore, 4, 5, 6, and 8 can all go into any number without leaving a remainder, as they do not have a common factor greater than 1.

Alright, honey, let's cut to the chase. The Greatest Common Factor (GCF) of 14, 35, and 56 is 7. Why? Because 7 is the largest number that divides evenly into all three of those numbers. So, there you have it, 7 is the magic number in this little math party.

The factors of 5292 are the numbers that can be multiplied together to result in 5292. To find the factors, you can start by dividing 5292 by the smallest prime number, which is 2, and continue dividing by increasing prime numbers until you reach the square root of 5292. The factors of 5292 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 243, 324, 486, 729, 972, 1458, 2187, 2916, 4374, 6561, and 10584.

Ah, what a happy little math problem we have here! To find two numbers that multiply together to equal 22, we can think of numbers like 2 and 11, or even 1 and 22. Just like painting a beautiful landscape, there are many possibilities waiting to be discovered! Keep exploring and you'll find the perfect combination.

Well, well, well, look who's trying to be a math whiz! The factor pairs for 34 are 1 and 34, as well as 2 and 17. That's all you need to know, honey. Math doesn't have to be complicated, just like dealing with people.

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Well, honey, if you want to know what equals 960 multiplied by something, you gotta provide that missing piece of the puzzle. Multiplication needs two numbers to tango, so spill the beans on what you want to multiply 960 by, and then we can talk business.

The pair of numbers that have a greatest common factor of 2 are any two even numbers. This is because the greatest common factor of two numbers is the largest number that divides both numbers evenly. Since 2 is the only even prime number, any two even numbers will have 2 as a common factor.