Factoring and Multiples

The Greatest Common Factor (GCF) of 90 and 180 is 90. To find the GCF, you can list the factors of each number and determine the largest number that divides both numbers evenly. The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180. The largest number that appears in both lists is 90, making it the Greatest Common Factor.

Oh, dude, let me break it down for you. The greatest common factor of 40 and 200 is 40. It's like the biggest number that both 40 and 200 can be divided by without leaving a remainder. So yeah, 40 is the winner here.

Oh, isn't that just lovely! When you look at the first 9 multiples of 11, you'll notice a beautiful pattern emerging. Each multiple increases by 11 from the previous one, creating a nice, steady progression that's as calming as painting happy little trees. Just take a moment to appreciate the harmony and order in those numbers, like little brushstrokes on a canvas.

Well, isn't that just a happy little math question! To find the greatest common factor of 234 and 208, we can look at the factors of each number. The factors of 234 are 1, 2, 3, 6, 9, 13, 18, 26, 39, 78, 117, and 234. The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208. The greatest common factor of 234 and 208 is 26.

Numbers that have both 5 and 3 as factors are multiples of both 5 and 3, which means they are multiples of the least common multiple (LCM) of 5 and 3. The LCM of 5 and 3 is 15, so any multiple of 15 will have both 5 and 3 as factors. Examples of such numbers include 15, 30, 45, 60, and so on.

The factor of ab refers to the numbers or variables that can be multiplied to produce the term ab. In this case, the factors of ab are a and b. Factors are numbers or variables that can divide into a term without leaving a remainder. Therefore, the factors of ab are a and b because they can be multiplied together to result in the term ab.

The numbers 5, 3, 4, and 7 do not have a common factor other than 1. Therefore, they do not go into a specific number as a group. Each of these numbers can only be divided by 1 and itself without leaving a remainder.

The factors of -10x are any two numbers or algebraic expressions that can be multiplied together to result in -10x. These factors could be -1 and 10x, 1 and -10x, -2 and 5x, 2 and -5x, and so on. In general, the factors of a number or expression are the values that divide it evenly without leaving a remainder.

To find the Greatest Common Factor (GCF) of 42 and 100, you need to determine the largest number that can evenly divide both 42 and 100. First, list the factors of each number: 42 (1, 2, 3, 6, 7, 14, 21, 42) and 100 (1, 2, 4, 5, 10, 20, 25, 50, 100). The GCF is the largest number that appears in both lists, which in this case is 2. Therefore, the GCF of 42 and 100 is 2.

Well, honey, let me tell you. The numbers that multiply to 294 are 2, 3, 7, and 7. Yep, you heard me right. 2 times 3 times 7 times 7 equals 294. So, there you have it, the sassy math answer you never knew you needed.

The common factors of 14 and 32 are the numbers that can evenly divide both 14 and 32 without leaving a remainder. The factors of 14 are 1, 2, 7, and 14, while the factors of 32 are 1, 2, 4, 8, 16, and 32. Therefore, the common factors of 14 and 32 are 1 and 2.

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCF of 126 and 189, we can use the prime factorization method. Prime factorizing 126 gives 2 x 3^2 x 7, and prime factorizing 189 gives 3^3 x 7. The common factors between the two numbers are 3 and 7. Therefore, the GCF of 126 and 189 is 21.

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

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

Prime Factors: 1, 2, 3, 5

Product of Prime Numbers: 2 x 3 x 5

3, 6, 15, 30

Oh, dude, the Highest Common Factor (HCF) for 540 and 630 is 90. It's like the cool kid that both 540 and 630 can hang out with without any drama. So yeah, 90 is the HCF for those numbers, keeping things chill in the math world.

Oh, dude, factors of 114? That's like asking me to list all the snacks I've ever eaten. Alright, let's do this. So, the factors of 114 are 1, 2, 3, 6, 19, 38, 57, and 114. Boom, there you go!

Oh, dude, the paperwork is a total drag. Like, who wants to deal with all those forms and emails, am I right? But hey, it's all part of the gig, I guess. Gotta pay the bills somehow, right?

70 has factors of 7 x 10

'7' is a prime number.

10 is a compound ( non-prime number) , because 10 = 2 x 5.

The only 3-digit number that has factors of 2 and 7 is 14. Factors are numbers that can be multiplied to give the number in question. In this case, 2 x 7 = 14, making 14 the only 3-digit number with factors of 2 and 7.

3

3.03

3.3

3.333

3.33 continuous

Well honey, the highest common factor of 120 and 160 is 40. It's like finding the biggest slice of cake you can share between the two numbers, and in this case, that slice is 40. So go ahead and slice up that math problem like a pro!

To find the Least Common Multiple (LCM) of 130 and 195, you first need to find the prime factorization of each number. The prime factorization of 130 is 2 x 5 x 13, and the prime factorization of 195 is 3 x 5 x 13. Then, you identify the common prime factors and their highest powers, which are 2, 3, 5, and 13. Finally, you multiply these common prime factors with their highest powers to find the LCM, which is 2 x 3 x 5 x 13 = 390.

Well, let's take a moment to appreciate these numbers. The Greatest Common Factor (GCF) is the largest number that divides evenly into all of them. If we look closely, we can see that the GCF for 35, 49, 70, and 84 is 7. It's like finding a happy little tree that connects them all together. Just remember, math is like painting a beautiful picture - sometimes you just need to step back and see the bigger picture to find the answer.

-5

Well, honey, the greatest common factor of 24, 40, and 64 is 8. It's like finding the hottest accessory that goes with all your outfits - in this case, 8 is the perfect match for these three numbers. So, go ahead and rock that GCF like the fashionista of math that you are!