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Factoring and Multiples
This category should include questions about greatest common factors and lowest common multiples.
63,380 Questions
The least common multiple (LCM) of 128 and 256 is the smallest number that is a multiple of both 128 and 256. To find the LCM, you can first determine the prime factors of each number. 128 = 2^7 and 256 = 2^8. The LCM is the product of the highest power of each prime factor that appears in either number, so LCM(128, 256) = 2^8 = 256.
What is the LCM of 145 and 250?
The Least Common Multiple (LCM) of 145 and 250 is the smallest positive integer that is divisible by both 145 and 250 without leaving a remainder. To find the LCM, we first need to find the prime factorization of each number. 145 = 5 x 29 and 250 = 2 x 5^3. Then, the LCM is calculated by taking the highest power of each prime factor that appears in either number, so LCM(145, 250) = 2 x 5^3 x 29 = 36250.
What are the common factors of 100 and 132?
The common factors of 100 and 132 are the numbers that can evenly divide both 100 and 132 without leaving a remainder. The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132. The common factors of 100 and 132 are 1, 2, 4.
What are numbers that have only two factors?
Numbers that have only two factors are called prime numbers. These numbers can only be divided by 1 and themselves without leaving a remainder. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. Prime numbers play a crucial role in number theory and cryptography due to their unique properties.
What is the sum of all common factors of 12 and 86?
To find the sum of all common factors of 12 and 86, we first need to determine the factors of each number. The factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 86 are 1, 2, 43, and 86. The common factors of 12 and 86 are 1 and 2. Therefore, the sum of all common factors of 12 and 86 is 1 + 2 = 3.
What are the factors and prime factors of 656?
1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 49, 56, 63, 72, 84, 98, 112, 126, 144, 147, 168, 196, 252, 294, 336, 392, 441, 504, 588, 784, 882, 1008, 1176, 1764, 2352, 3528, 7056
2, 3 and 7 are prime.
What is the greatest common factor of 8x and 28?
Well, isn't that just a happy little question! The greatest common factor of 8x and 28 is 4. You see, we can break down 8x into 4 * 2 * x and 28 into 4 * 7, and the highest factor they have in common is 4. Just remember, there are no mistakes, just happy little accidents in math!
How do you split the alphabet into 4 equal groups?
To split the alphabet into 4 equal groups, you would first need to determine the total number of letters in the alphabet, which is 26. Then, divide 26 by 4 to get 6 with a remainder of 2. This means the first three groups would have 6 letters each, and the fourth group would have 8 letters. The groups would be as follows: ABCDEF, GHIJKL, MNOPQR, STUVWXYZ.
To find the Greatest Common Factor (GCF) of 22, 33, and 55, we first need to factorize each number. The factors of 22 are 2 x 11, the factors of 33 are 3 x 11, and the factors of 55 are 5 x 11. The common factor among these three numbers is 11, making it the Greatest Common Factor (GCF) of 22, 33, and 55.
What is the greatest common factor of 42 70 and 105?
To find the greatest common factor (GCF) of 42, 70, and 105, we first need to find the prime factorization of each number.
42 = 2 x 3 x 7 70 = 2 x 5 x 7 105 = 3 x 5 x 7
The GCF is the product of the common prime factors raised to the lowest power they appear in all three numbers. Therefore, the GCF of 42, 70, and 105 is 7.
Oh, dude, you're hitting me with the math questions, huh? Alright, let me just casually drop this knowledge bomb on you - 56 times 70 equals 3920. Boom, math wizard right here. Like, no big deal or anything.
What numbers have exactly 2 factors under 10?
Numbers that have exactly 2 factors under 10 are prime numbers. Prime numbers are integers greater than 1 that have no positive divisors other than 1 and themselves. Examples of prime numbers under 10 are 2, 3, 5, and 7. These numbers have only two factors, 1 and the number itself.
What is the GCF of 32 56 and 96 using prime factorizations?
2 x 2 x 2 x 2 x 2 = 32
2 x 2 x 2 x 7 = 56
2 x 2 x 2 x 2 x 3 = 96
2 x 2 x 2 = 8, the GCF
What are the common factors of 40 and 45?
The common factors of 40 and 45 are the numbers that can evenly divide both 40 and 45 without leaving a remainder. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. The factors of 45 are 1, 3, 5, 9, 15, and 45. The only common factor of 40 and 45 is 5.
What is the LCM of 396 and 495?
Well, honey, the Least Common Multiple (LCM) of 396 and 495 is 1980. It's like finding the smallest number that both 396 and 495 can divide into evenly without leaving a remainder. So, there you have it, darling, 1980 is the magic number you're looking for.
The Highest Common Factor (HCF) of 6 and 18 is the largest number that divides both 6 and 18 without leaving a remainder. To find the HCF, we need to determine the common factors of 6 and 18, which are 1, 2, and 3. The largest among these common factors is 3, so the HCF of 6 and 18 is 3.
What are the multiples of 9 to 9000?
To find the multiples of 9 up to 9000, you can use the formula: (9 \times n), where (n) is a positive integer. The first few multiples of 9 are 9, 18, 27, 36, and so on. To find the multiples of 9 up to 9000, divide 9000 by 9, which equals 1000. Therefore, the multiples of 9 up to 9000 are all the multiples of 9 from 9 to 9000, inclusive.
How many times can 2 go into 0?
In mathematics, division by zero is undefined, as it leads to mathematical inconsistencies. Therefore, 2 cannot be divided into 0 any number of times. This is because division is the inverse operation of multiplication, and there is no number you can multiply by 2 to get 0 as the result.
What are the multiples of 35 from 1 to 1000?
Oh, what a happy little question! To find the multiples of 35, we simply need to skip count by 35. So, starting from 35, the multiples would be 70, 105, 140, and so on, all the way up to 980. Just imagine each multiple as a little tree in a vast forest of numbers, each one unique and special in its own way.
What is the least common multiple of 72 196 and 240?
To find the least common multiple (LCM) of 72, 196, and 240, we first need to prime factorize each number.
72 = 2^3 * 3^2 196 = 2^2 * 7^2 240 = 2^4 * 3 * 5
Next, we take the highest power of each prime factor that appears in any of the factorizations: 2^4 * 3^2 * 5 * 7^2 = 10080.
Therefore, the least common multiple of 72, 196, and 240 is 10080.
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Is the LCM of a prime number and a composite number a multiple of the prime number?
If the GCF of two numbers is 1, their LCM will be their product. Such numbers are called relatively prime, or co-prime. Any two prime numbers (like 3 and 5) will be that way, but the numbers don't have to be prime (like 4 and 9).
