Factoring and Multiples

Well, well, well, look who's trying to factor a quadratic equation! To factor 2x^2 + 11x + 14, you need to find two numbers that multiply to 28 (2*14) and add up to 11. Those numbers are 2 and 14. So, the factored form is (2x + 7)(x + 2). Voila!

The longest factor string for 42 is when we break down 42 into its prime factors. 42 can be expressed as 2 x 3 x 7. This is the longest factor string because these are the prime numbers that, when multiplied together, result in 42.

3 (if "between 3-200" includes 3), 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, and 198 are all multiples of 3 between 3 and 200.

The greatest common factor (GCF) of 48 and 60 is the largest number that divides both 48 and 60 without leaving a remainder. To find the GCF, you can list the factors of each number and identify the largest factor they have in common. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, while the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The largest factor that both 48 and 60 share is 12, making the GCF of 48 and 60 equal to 12.

To find the common monomial factor of a set of monomials, first identify the variables and their corresponding exponents in each monomial. Next, determine the smallest exponent for each variable that appears in all the monomials. Finally, combine the variables with their corresponding smallest exponents to form the common monomial factor. This factor will be the largest monomial that can be factored out from each original monomial.

Numbers that can be divided into 3 and 4 without a remainder are multiples of both 3 and 4, which are also known as common multiples. The least common multiple of 3 and 4 is 12, so any number that is a multiple of 12 can be divided by both 3 and 4 without a remainder. This includes numbers like 12, 24, 36, 48, and so on.

Well, well, well, look who's trying to flex their math muscles! The least common multiple of 100 and 125 is 500. You're welcome for the knowledge drop, honey.

The greatest common factor of 133 and 203 is 7

Oh, what a happy little question! To find the greatest common factor of 280 and 332, we can first list the factors of each number. The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280, while the factors of 332 are 1, 2, 4, 83, 166, and 332. The greatest common factor is the largest number that appears in both lists, which in this case is 4.

The GCF of 16 and 81 is 1.

16's prime factors are 2, 2, 2 and 2

81's prime factors are 3, 3, 3 and 3

Therefore, they do not have any common prime factors, and so the greatest common factor is 1.

Well, isn't that a happy little question! The greatest common factor of 38 and 48 is 2. You see, the greatest common factor is the largest number that divides evenly into both 38 and 48, and in this case, 2 is that special number. Just like painting a beautiful landscape, finding the greatest common factor is all about looking for the common elements that bring everything together in harmony.

To determine if 3 is a factor of 261, we need to check if 261 is divisible by 3 without any remainder. We can do this by dividing 261 by 3. When we divide 261 by 3, we get 87 with no remainder. Therefore, 3 is a factor of 261 because it divides evenly into 261.

the answer is -9....

The Greatest Common Factor (GCF) of 36, 64, and 72 is 4, as it is the largest number that divides evenly into all three numbers. The Least Common Multiple (LCM) of 36, 64, and 72 is 576, as it is the smallest multiple that is divisible by all three numbers. The GCF is found by identifying the common factors of the numbers and selecting the largest one, while the LCM is determined by multiplying the prime factors of the numbers.

To factor out the greatest common factor from the given expression 14cd - 7c, we first identify the common factors of the coefficients and variables. The greatest common factor of 14 and 7 is 7, and the common factor of c is c. Therefore, we can factor out 7c from both terms to get 7c(2d - 1).

Oh, dude, ordering decimals is like ordering a sandwich, but with numbers. So, you start by looking at the biggest part of the number, which is the whole number part. In this case, 13 is the biggest whole number. Then you move on to the decimal part, and you just compare the numbers after the decimal point. So, the order would be 13,351; 12,353; 1,235; and 13.

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 168 and 252, we first list the factors of each number: 168 (1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168) and 252 (1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252). The common factors are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. Therefore, the HCF of 168 and 252 is 84.

The factors of 81 are 1, 3, 9, 27, and 81.

The factor pairs of 81 are 1 x 81, 3 x 27, and 9 x 9.

The proper factors of 81 are 1, 3, 9, and 27, or if the definition you are using excludes 1, they are 3, 9, and 27.

The prime factors of 81 are 3, 3, 3, and 3.

Note: There is repetition of these factors, so if the prime factors are being listed instead of the prime factorization, usually only the distinct prime factors are listed.

The distinct prime factor of 81 is 3.

The prime factorization of 81 is 3 x 3 x 3 x 3 or in exponential form 34. 81 = 3*3*3*3 or 3^4.

The factors of 495 are the numbers that can be evenly divided into 495 without leaving a remainder. The factors of 495 are 1, 3, 5, 9, 15, 33, 45, 99, 165, and 495. These numbers are all whole numbers that, when multiplied together, result in 495.

21, & 28.

Because

7 x 3 = 21

7 x 4 = 28

To determine how many ninths make up one third, we need to first convert one third into ninths. Since one third is equivalent to three ninths (3/9), we can conclude that three ninths make up one third. This is because both fractions represent the same proportion of a whole, with three parts out of a total of nine parts being equivalent to one third.

Oh, dude, you're hitting me with the math questions, huh? So, a 2-digit number with 10 factors would be 60. Why? Because it has factors 1, 2, 3, 4, 5, 6, 10, 12, 15, and 30. Boom, math wizardry at its finest!

The factors of 18 are:

1, 2, 3, 6, 9, 18

The factors of 48 are:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 72 are:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

The common factors are:

1, 2, 3, 6

Oh, what a happy little math question! To find the greatest common factor of 90, 105, and 165, we first need to find the factors of each number. Then, we look for the largest number that divides evenly into all three. Let's paint a picture together and discover that the greatest common factor of 90, 105, and 165 is 15. Keep up the good work, there are no mistakes in math, just happy little numbers!