0
Factoring and Multiples
This category should include questions about greatest common factors and lowest common multiples.
63,380 Questions
How many integers between 13 and 19 inclusive have an even number of prime factors?
13 is prime
14=2x7, 2 factors
15=3x5, 2 factors
16=24, 4 factors
17 is prime
18=2x32, 3 factors
19 is prime
So the answer is 3 (14, 15 and 16)
How do you make 27 using 1 2 3 and 4 only once?
To make 27 using the numbers 1, 2, 3, and 4 only once, you can use the following mathematical expression: (3 * 4) + (2 * 1) = 12 + 2 + 1 = 27. This equation follows the order of operations (multiplication before addition) to correctly arrive at the desired result of 27.
Oh, dude, 0.835 as a fraction is 835/1000. You know, like, you just move the decimal point three places to the right to get the numerator, and the denominator is always 1000 because decimals are just fancy fractions in disguise. So yeah, 0.835 is 835/1000. Easy peasy.
What multiples of 10 is 34 between?
Well, darling, 34 is snug as a bug between the multiples of 10, specifically 30 and 40. So, it's not quite cozy with the 10s, but it's definitely hanging out in the neighborhood.
What is the percent of prime numbers from 1-100?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are the prime numbers in this range, and there are 25 of them. So, of the 100 numbers, 25 are pime, giving us 25%.
What is the GCF of 72 144 and 192?
Well, let's take a moment to appreciate these numbers, like happy little trees on our canvas. To find the Greatest Common Factor (GCF), we look for the largest number that divides evenly into all three numbers. In this case, the GCF of 72, 144, and 192 is 24, which is like a strong foundation for our mathematical masterpiece.
Are all multiples of 6 also multiples of 12?
Well, honey, if you paid attention in math class, you'd know that yes, all multiples of 6 are also multiples of 12. Why? Because 12 is a multiple of 6, so any number that is a multiple of 6 will also be a multiple of 12. It's simple math, darling.
Oh, isn't that a happy little question? To find the Least Common Multiple (LCM) of 35, 65, and 90, we can start by listing the prime factors of each number. Then, we can take the highest power of each prime factor that appears in any of the numbers. By doing this, we find the LCM, which is like a beautiful harmony of these numbers coming together. Just like how different colors blend on a canvas to create a masterpiece!
What is the greatest common factor of 84 and 154 and 168?
Well, honey, the greatest common factor of 84, 154, and 168 is 14. It's like finding the common ground between three drama queens - you gotta find the biggest number that can divide them all without any fuss. So, just grab that 14 and call it a day, darling!
773 is a prime number, meaning it is only divisible by 1 and itself. It is not the result of a simple mathematical operation like addition, subtraction, multiplication, or division. Therefore, 773 is equal to itself, as it is a unique number with no factors other than 1 and 773.
What are the factors of 16 24 and 56?
The factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56. These factors are the numbers that can evenly divide the given numbers without leaving a remainder.
Express 72 as a product of its prime factors?
To express 72 as a product of its prime factors, we first identify the prime numbers that can divide evenly into 72. We start by dividing 72 by the smallest prime number, 2, which gives us 36. Then, we divide 36 by 2 again to get 18. Next, we divide 18 by 2 to get 9. Finally, we divide 9 by 3 to get 3. Therefore, the prime factors of 72 are 2 x 2 x 2 x 3 x 3.
To find the least common multiple (LCM) of 2, 9, and 18, we first need to factorize each number into its prime factors.
2 = 2^1 9 = 3^2 18 = 2^1 * 3^2
Next, we take the highest power of each prime factor that appears in any of the numbers: 2^1 and 3^2.
Multiplying these prime factors together, we get LCM(2, 9, 18) = 2^1 * 3^2 = 2 * 9 = 18.
Therefore, the LCM of 2, 9, and 18 is 18.
What are the multiples of 7 between 40 and 60?
The multiples of 7 between 40 and 60 are 42, 49, and 56.
What are the factors and prime factors of 511?
The factors of 511 are the numbers that can be multiplied together to give 511. The factors of 511 are 1, 7, 73, and 511. Prime factors are the factors that are prime numbers. The prime factors of 511 are 7 and 73, as they are the prime numbers that can be multiplied together to give 511.
Oh honey, the LCM of 14, 21, and 27 is 378. It's like finding the lowest common denominator at a family reunion - you just gotta pick the biggest number that they can all agree on. So, 378 it is, darling!
You can't.
x4 + y4 is irreducible.
It's (x+yi^1.5)(x+yi^0.5)(x-yi^1.5)(x-yi^0.5). You use the equation x^2-y^2=(x+y)(x-y) and x^2+y^2=(x+yi)(x-yi).
*Edit This IS reducible.
X^4+Y^4=X^4+Y^4+2X^2Y^2 -2X^2Y^2 I add and minus 2X^2Y^2 so the value stays the same.
X^4+Y^4+2X^2Y^2=(X^2+Y^2)^2
So it equals to (X^2+Y^2)^2-2X^2Y^2.
Then, we factor using difference of squares.
(X^2+Y^2)^2-2X^2Y^2=(X^2+Y^2+sqrt2 XY)(X^2+Y^2-sqrt2 XY)
*Note the XY is not included in the sqrt sign
What is the sum of all the common factors of 99 and 33?
To find the common factors of 99 and 33, we first need to find the factors of each number. The factors of 99 are 1, 3, 9, 11, 33, and 99. The factors of 33 are 1, 3, 11, and 33. The common factors are 1, 3, and 11. Adding these common factors together gives us 1 + 3 + 11 = 15. Therefore, the sum of all the common factors of 99 and 33 is 15.
What is the highest common factor of 33 77 and 132?
To find the highest common factor (HCF) of 33, 77, and 132, we first need to find the prime factors of each number. The prime factors of 33 are 3 and 11, the prime factors of 77 are 7 and 11, and the prime factors of 132 are 2, 3, 11. To find the HCF, we look for the common prime factors among the numbers, which are 11. Therefore, the highest common factor of 33, 77, and 132 is 11.
What is the hcf of 1225 and 700?
Oh, isn't finding the highest common factor a joyful journey? Let's take a moment to appreciate the beauty of numbers coming together. The highest common factor of 1225 and 700 is 175, bringing harmony and unity to these two numbers. Just like in painting, when different elements blend perfectly, creating a masterpiece.
How can you write 34 as a product of prime factors?
Oh, dude, writing 34 as a product of prime factors is like breaking down a math problem while trying not to fall asleep. So, you start by dividing 34 by the smallest prime number, which is 2, and you get 17. Then, you're left with 17, which is already a prime number, so that's it. 34 written as a product of prime factors is 2 x 17. Easy peasy, lemon squeezy.
Which Numbers between 1-25 have an odd number of factors?
Oh, dude, let me break it down for you! Numbers with an odd number of factors are called "square numbers." So, in the range of 1-25, the square numbers are 1, 4, 9, and 25. These numbers have factors like 1, the number itself, and the square root, giving them an odd number of factors. So, like, those are the ones you're looking for!
