Factoring and Multiples

To express the number 1269 as a product of prime factors, we need to find its prime factors. We start by dividing it by the smallest prime number, which is 2. 1269 ÷ 2 = 634.5, which is not a whole number. Moving on to the next prime number, 3, we find that 1269 ÷ 3 = 423. Continuing this process, we find that 423 ÷ 3 = 141, and 141 ÷ 3 = 47. Therefore, the prime factorization of 1269 is 3 x 3 x 47.

Well, isn't that just a happy little math question? Let's find the Greatest Common Factor (GCF) of 72 and 170. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The factors of 170 are 1, 2, 5, 10, 17, 34, 85, and 170. The largest number that appears in both lists is 2, so the GCF of 72 and 170 is 2.

Oh, dude, you're hitting me with the math questions, huh? Well, the common factors of 27 and 45 are 1, 3, and 9. So, like, those are the numbers that both 27 and 45 can be divided by without leaving a remainder. Math, man, it's like a secret language or something.

The highest common factor (HCF) of 48 and 72 is 24. To find the HCF, you can list the factors of each number and identify the largest number that both 48 and 72 share. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, while the factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. The largest number that appears in both lists is 24, making it the HCF.

The factor that does not belong in the sequence is 1. The sequence follows a pattern of multiplying by 2: 2 x 2 = 4, 4 x 2 = 8, 8 x 2 = 16. However, 1 does not fit this pattern and disrupts the sequence.

The Highest Common Factor (HCF) of 8 and 13 is 1. This is because 8 and 13 are both prime numbers, meaning they have no common factors other than 1. In other words, there are no integers other than 1 that can divide both 8 and 13 without leaving a remainder.

The factors of 6Ab^2 are the numbers or variables that can be multiplied together to result in 6Ab^2. In this case, the factors of 6Ab^2 are 1, 2, 3, 6, A, B, A^2, B^2, AB, 2A, 3A, 6A, 2B, and 3B. These factors can be combined in various ways to represent the original expression 6Ab^2.

Repeated division is a mathematical operation where a number is divided by another number multiple times. This process involves dividing the quotient of the previous division by the divisor again, and so on. It is commonly used in various mathematical concepts such as finding factors, prime factorization, and simplifying fractions.

The most common Kwikset SmartKey problem reported by users is difficulty in rekeying the lock or the key not turning smoothly in the lock.

Oh honey, 36 is neither a factor nor a multiple of 24. Factors are numbers that can be multiplied to give you a certain number, and multiples are just what you get when you keep adding that number. 36 just doesn't fit the bill for either with 24, so they're not meant to be together.

To find the greatest common factor (GCF) of 9s and 63s to the third power, we first need to factor out the common factors of the two numbers. The prime factorization of 9s is 3 * 3 * s, and the prime factorization of 63s^3 is 3 * 3 * 7 * s * s * s. The common factors between the two numbers are 3 * 3 * s, which simplifies to 9s. Therefore, the GCF of 9s and 63s^3 is 9s.

Well, darling, the least common multiple of 4, 10, and 25 is 100. It's like finding the smallest number that these three can all cozy up to without any drama. So, there you have it - 100 is the magic number that keeps these three in check.

Well, honey, a number that both 234 and 5 go into is 2340. You see, 234 is a multiple of 5 because it ends in 0, so any multiple of 234 will also be divisible by 5. So, grab a calculator and do the math if you don't believe me!

Oh, dude, the Least Common Multiple (LCM) of 2, 8, and 14 is 56. It's like the smallest number that all three of those numbers can divide into evenly without leaving a remainder. So, if you ever need to find a number that can handle 2, 8, and 14 without any drama, it's 56.

Oh, dude, you're hitting me with some math lingo now? Alright, so the prime factorization of 720 is 2^4 * 3^2 * 5. That's like breaking down a big number into its prime factors, so you can see what it's made of. Math can be fun, right?

The main difference between 12-2 and 12-3 electrical wiring cables is the number of conductors they contain. 12-2 cable has two conductors (black and white) and a ground wire, while 12-3 cable has three conductors (black, red, and white) and a ground wire. The additional conductor in 12-3 cable allows for more complex electrical circuits to be created.

The main difference between 12/2 and 12/3 wiring is the number of conductors they have. 12/2 wiring has two conductors (usually black and white) and a ground wire, while 12/3 wiring has three conductors (usually red, black, and white) and a ground wire. The extra conductor in 12/3 wiring allows for an additional circuit or a multi-wire branch circuit. This can impact electrical installations by providing more flexibility in the types of circuits that can be installed and allowing for more complex electrical setups.

Well, isn't that just a happy little math question! Let's take a look at these expressions together. The factors of 3x - 2y are (3x - 2y) and 1, while the factors of 3x + 2y are (3x + 2y) and 1. Remember, in math, factors are numbers or expressions that can be multiplied together to get a specific result. Just like painting, math can be a beautiful and creative process!

Oh, isn't that just lovely? The first four multiples of 11 are 11, 22, 33, and 44. Just imagine those numbers dancing together in harmony, creating a beautiful sequence that follows the rhythm of multiplication. Keep exploring those multiples, and you'll uncover even more delightful patterns in the world of numbers.

Well, honey, there are plenty of ways to make 135. You could have 135 one-dollar bills, 27 five-dollar bills, or even 45 three-dollar bills. Heck, you could even have a combination of different bills and coins to add up to 135. As long as it all adds up, you're good to go!

The prime factorization of a number breaks it down into its prime factors. In the case of 45, it can be expressed as 3 x 3 x 5. This is because 45 can be divided by 3 twice and by 5 once, resulting in the prime factors of 3 and 5. This prime factorization represents the unique combination of prime numbers that, when multiplied together, equal 45.

0.5

The multiples of 3 to 99 are the following:3,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96 and 99 1 and 100 is not a multiple of 3 so it should be from 3 to 99 :)

The factors of 30 are: 1 2 3 5 6 10 15 30.

The factors of 50 are: 1 2 5 10 25 50.

The common factors of 30 and 50 are: 1 2 5 10.

The greatest common factor of 30 and 50 is: 10.