Factoring and Multiples

The highest common factor (HCF) of 228 and 285 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, you can use the Euclidean algorithm. First, divide the larger number (285) by the smaller number (228) to get a quotient of 1 with a remainder of 57. Then, divide the previous divisor (228) by the remainder (57) to get a quotient of 4 with a remainder of 0. Therefore, the HCF of 228 and 285 is 57.

Well, darling, the highest common factor of 33 and 132 is 33. It's like finding the biggest slice of cake you can share between the two numbers - and in this case, that slice is 33. So, there you have it, the sassy math answer you never knew you needed.

Well, isn't that a happy little math question! To find the Least Common Multiple (LCM) of 2, 10, and 12, we look for the smallest number that all three numbers can divide into evenly. The LCM of 2, 10, and 12 is 60. Just like painting a beautiful landscape, finding the LCM is all about bringing different elements together in harmony.

The factors of 20 are: 1, 2, 4, 5, 10, and 20.

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24.

The factors common to 20 and 24 are: 1, 2, and 4.

The greatest factor common to 20 and 24 is: 4.

The common factors of 36 and 54 are the numbers that can evenly divide both 36 and 54 without leaving a remainder. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The common factors of 36 and 54 are 1, 2, 3, 6, 9, 18.

Oh, what a happy little math problem we have here! To factorize 6xy - 15y^2, we first look for the greatest common factor, which in this case is 3y. So we can rewrite the expression as 3y(2x - 5y). And just like that, we've created a beautiful factorized expression that brings a sense of harmony and balance to our mathematical canvas.

900

Some common factors that confuse homeowners about attic insulation include understanding the right type of insulation to use, determining the proper amount needed for their specific attic space, and knowing how to properly install and maintain the insulation for maximum effectiveness.

Well, isn't that a happy little math question you've got there! The greatest common factor for 35 and 100 is 5. You see, the greatest common factor is the largest number that divides evenly into both 35 and 100, and in this case, that number is 5. Just like painting, finding the greatest common factor is all about looking for the beautiful harmony between numbers.

Well, isn't that a happy little math problem! Let's see, to find two numbers that multiply together to make 154, we can think about breaking down 154 into its factors. One pair of numbers that works is 11 and 14. Just like painting a beautiful landscape, sometimes all it takes is a little patience and a gentle touch to find the answer you're looking for.

To find two numbers that multiply to 384, we need to factorize 384. The prime factorization of 384 is 2^7 * 3. To find the pair of numbers, we need to pair up these factors in a way that the multiplication of the pairs equals 384. One possible pair is 2^4 * 24, which equals 384. Therefore, the two numbers are 16 and 24.

Oh, isn't that just a happy little math question? Let's find the greatest common factor of 18, 24, and 40 together. First, we list the factors of each number and then find the largest number that divides evenly into all three. It looks like the greatest common factor of 18, 24, and 40 is 2.

See method below:

Number of times each prime factor

appears in the factorization of :

Prime

Factor Number

72 Number

120 Number

144 G.C.F

2 3 3 4 3

3 2 1 2 1

5 0 1 0 0

GCF = 2 cubed (2 times 2 times 2)= 8. 8 times 3 = 24

Therefore the HCF of 72 120 and 144 is 24

Use Number sense Write 2 numbers that cannot be divided evenly by 8 or 9.

The Greatest Common Factor of 18, 36, and 45 is 9

Oh, dude, factors of negative 15? Like, negative 1, 1, negative 3, 3, negative 5, and 5. It's like a party of numbers hanging out with negative 15, causing some math drama. So, yeah, those are the factors, but don't let them stress you out too much, man.

The prime factorisation of the square root of 99856 is 2*2*79.

The factors of 90 are the numbers that can be multiplied together to equal 90. These factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Factors always come in pairs, with one factor being less than or equal to the square root of the number and the other factor being greater.

Oh, dude, 92 is like 2 x 2 x 23. So, the prime factorization of 92 is 2^2 x 23. Just a couple of twos hanging out with a 23, no big deal.

To find the prime factorization of 48 using a factor tree, we start by breaking down 48 into its factors, such as 2 and 24. Then, we continue breaking down 24 into 2 and 12, and 12 into 2 and 6. Finally, we break down 6 into 2 and 3. This gives us the prime factorization of 48 as 2^4 * 3.

311

Yes, 42 is a multiple of 3. A multiple of a number is the result of multiplying that number by an integer. In this case, 3 multiplied by 14 equals 42, making it a multiple of 3.

The factors of 14 and 21 are:

14: 1,2,7,14

21:1,3,7,21

The common factors are:1 and 7. Therefore 7 is the greatest common factor (GCF)

Well, isn't that just a happy little math question! The Greatest Common Factor, or GCF, is the largest number that divides evenly into both 105 and 231. So, when we look at 105 and 231, we see that the GCF is 21. It's like finding a common ground where both numbers can be their best selves together.

To find the greatest common factor (GCF) of 52, 156, and 169, we need to first factor each number. The factors of 52 are 1, 2, 4, 13, 26, and 52. The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156. The factors of 169 are 1, 13, and 169. The GCF is the largest number that is a factor of all three numbers, which in this case is 13.