Factoring and Multiples

Oh, dude, you're hitting me with the math questions? Alright, let's see... the common factors of 112 and 240 are 1, 2, 4, 8, and 16. So, like, those are the numbers that can divide both 112 and 240 without leaving a remainder. Math is cool and all, but, like, can we talk about something more exciting?

To compare the sizes of fractions, it's helpful to find a common denominator. In this case, the common denominator is 12. When both fractions are converted to have a denominator of 12, 3/4 becomes 9/12 and 4/6 becomes 8/12. Therefore, 3/4 (9/12) is bigger than 4/6 (8/12) because 9/12 is greater than 8/12.

Oh, dude, you're hitting me with some math now? Alright, let me just casually tell you that 500,000 can be written as 500 x 1000. So, technically, 500 times 1000 equals 500,000. But like, who even multiplies numbers these days, am I right?

To find the Least Common Multiple (LCM) for 20, 14, and 10, you first need to list the prime factors of each number: 20 = 2^2 * 5, 14 = 2 * 7, and 10 = 2 * 5. Then, identify the highest power of each prime factor that appears in any of the numbers: 2^2, 5, and 7. Finally, multiply these factors together to find the LCM: LCM(20, 14, 10) = 2^2 * 5 * 7 = 140.

The common factors of 99 and 121 are the numbers that can evenly divide both 99 and 121 without leaving a remainder. The factors of 99 are 1, 3, 9, 11, 33, and 99. The factors of 121 are 1, 11, and 121. Therefore, the only common factor of 99 and 121 is 1.

Well, isn't that just a happy little question! When we talk about numbers that 8 can go into evenly, we're looking for numbers that 8 can divide without leaving any remainder. So, numbers like 16, 24, 32, and so on are some examples where 8 can fit in just perfectly, like a cozy little puzzle piece. Just remember, there's no mistakes, just happy little numbers waiting to be divided evenly by 8.

Estimating 25 78 as 25 75 is a common rounding technique used to simplify calculations while maintaining a reasonable level of accuracy. By rounding to the nearest multiple of 5 or 10, it makes mental math easier and quicker to perform. This approximation can be especially useful in situations where precise values are not necessary, such as in informal calculations or when making quick estimations.

The three main factors that cause erosion are water, wind, and ice. Water erosion occurs when moving water, such as rivers or ocean waves, wears away soil and rock. Wind erosion happens when strong winds carry and deposit soil particles in a different location. Ice erosion, also known as glacial erosion, occurs when glaciers move across the land, scraping and carrying away rocks and soil.

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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.

Since 23 is a single number, you could say that it shares all of its factors with itself. So the greatest factor of 23 is 23

The multiples of 7 greater than 48 but less than 91 are 49, 56, 63, 70, 77, 84. To find these multiples, you start by dividing 48 by 7 to get the closest whole number, which is 6. Then, you add 1 to that number to get the next multiple, which is 7. You continue this pattern until you reach the upper limit of 91.

Oh honey, the greatest common factor of 8 and 21 is 1. Those two numbers couldn't be more different if they tried. It's like trying to find common ground between a cat and a dog - just not gonna happen.

To find 3/4 of 480, you multiply 480 by 3/4. This can be calculated by multiplying 480 by 3 and then dividing the result by 4.

(480 x 3) / 4 = 1440 / 4 = 360.

Therefore, 3/4 of 480 is 360.

A 5-digit number that is divisible by 9 must have its digits sum to a multiple of 9. The smallest 5-digit number that fits this criterion is 10,008 (1 + 0 + 0 + 0 + 8 = 9). Other examples include 10,017, 10,026, and so on, up to the largest 5-digit number that is divisible by 9, which is 99,999.

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The Highest Common Factor (HCF) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF of 245 and 392, you would first factorize both numbers: 245 = 5 x 7 x 7 and 392 = 2 x 2 x 2 x 7 x 7. Then, identify the common factors between the two numbers, which are 7 and 7. Therefore, the HCF of 245 and 392 is 7 x 7 = 49.

540 = 2 x 2 x 3 x 3 x 3 x 5

The common multiples of 3 and 6 are numbers that can be divided evenly by both 3 and 6. The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on. The multiples of 6 are 6, 12, 18, 24, 30, and so on. Therefore, the common multiples of 3 and 6 are numbers that appear in both lists, such as 6, 12, 18, 24, and 30.

To simplify the fraction 360/540, you need to find the greatest common factor (GCF) of both numbers, which is 180. Divide both the numerator and denominator by 180 to simplify the fraction. This results in 360/540 simplifying to 2/3.

The common factors of 35 and 60 are 1 and 5.

The first common multiple of 4, 5, and 10 is their least common multiple (LCM), which is the smallest number that is a multiple of all three numbers. The LCM of 4, 5, and 10 is 20. The next common multiple would be the next multiple of 20, which is 40. The third common multiple would be the next multiple of 20, which is 60.

Oh, what a lovely question! Let's find some happy little multiples here. The first three common multiples of 2, 3, and 9 are 18, 36, and 54. Isn't it wonderful how numbers can come together in harmony like this? Just like painting a beautiful landscape, math can be a peaceful and joyful experience.

Well, isn't that a happy little mystery to solve! If you have 3 factors and their sum is 7, you must be the number 1, 2, and 4. Each number plays its own special role in creating that sum, just like how each color on our palette adds to the beauty of a painting. Keep exploring and discovering, my friend!

To find the greatest common factor (GCF) of two numbers, you need to determine the largest number that divides evenly into both numbers. To find the GCF of 510 and 2430, you can first list the factors of each number. The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, and 510. The factors of 2430 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 243, 270, 405, 486, 810, 1215, and 2430. The greatest common factor of 510 and 2430 is 30.