Factoring and Multiples

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.

Oh, dude, you're hitting me with some math vibes. So, the factors of 81 are 1, 3, 9, 27, and 81. And if you want to talk prime factors, well, 81 is just 3 to the power of 4. So, like, the prime factors of 81 are 3, 3, 3, and 3. Math can be funky, right?

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 common factors of 18, 48, and 72 are the numbers that can evenly divide all three of these numbers. To find the common factors, you first need to find the prime factorization of each number. The prime factorization of 18 is 2 x 3^2, 48 is 2^4 x 3, and 72 is 2^3 x 3^2. The common factors are the shared prime factors among all three numbers, which in this case are 2 and 3.

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!

Well, isn't that a happy little question! To find the highest common factor of 84 and 154, we can start by listing the factors of each number. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. The factors of 154 are 1, 2, 7, 11, 14, 22, 77, and 154. The highest common factor, also known as the greatest common divisor, of 84 and 154 is 14.

Sweetheart, .5 fl. oz is bigger than .34 fl. oz. It's like asking if a teacup is bigger than a shot glass - common sense, right? So go ahead and pour yourself that extra .16 fl. oz of whatever you're measuring, you deserve it.

Oh, dude, the greatest common factor of 50 and 160 is 10. It's like the cool kid at the party that both 50 and 160 want to hang out with. So yeah, 10 is the number that can divide both 50 and 160 without any drama.

Yes, prime factorization is not an NP-complete problem. It is in fact in the complexity class NP, but it is not known to be NP-complete.

A set can be proven to be infinite if it can be put into a one-to-one correspondence with a proper subset of itself. This means that there is a way to match each element in the set with a unique element in a subset, showing that the set has an endless number of elements.

One can demonstrate that a set is infinite by showing that it can be put into a one-to-one correspondence with a proper subset of itself. This means that the set can be matched with a part of itself without running out of elements, indicating that it has an infinite number of elements.

Finding the least common multiple (LCM) would help when dividing items into equal groups by ensuring that each group receives an equal number of items without any remainders. By determining the LCM of the total number of items and the number of groups, you can divide the items evenly among the groups. This method helps to avoid any discrepancies in the distribution of items and ensures a fair division process.

The Highest Common Factor (HCF) of 55, 77, and 132 is the largest number that divides all three numbers without leaving a remainder. To find the HCF, you can first find the prime factors of each number: 55 = 5 x 11, 77 = 7 x 11, and 132 = 2^2 x 3 x 11. Then, identify the common prime factors among the numbers, which are 11. Therefore, the HCF of 55, 77, and 132 is 11.

Numbers with only one factor are called prime numbers. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. Examples of prime numbers include 2, 3, 5, 7, 11, and so on. These numbers have only two factors: 1 and the number itself.

LCM = 168

The Highest Common Factor (HCF) of 210 and 112 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, you can use the Euclidean algorithm or prime factorization method. In this case, the prime factorization of 210 is 2 x 3 x 5 x 7, and the prime factorization of 112 is 2^4 x 7. The common factors are 2 and 7, so the HCF is 2 x 7 = 14.

To find the greatest common factor (GCF) of 34, 51, and 85, we first need to find the prime factorization of each number. The prime factorization of 34 is 2 x 17, 51 is 3 x 17, and 85 is 5 x 17. The common factor among these three numbers is 17, making the GCF of 34, 51, and 85 equal to 17.

These do: 1, 2, 3, 5, 6, 10, 15, 30.

Oh, dude, you've thrown me back to high school math class with that one. So, X2 - 16x + 28 is a quadratic expression that can be factored as (X - 14)(X - 2). That's like the math version of solving a puzzle, but like, who even uses this stuff in real life, am I right?

103 can be expressed as the sum of two prime numbers (53 + 50) or the product of two prime numbers (17 x 6 + 1). It can also be written as the cube of the fourth prime number (2^3 + 11^3) or as the sum of consecutive numbers (51 + 52).