Factoring and Multiples

The greatest common factor of 16 and 25 is 1. This is because 1 is the largest integer that divides both 16 and 25 without leaving a remainder. 16 can be factored into 2^4 and 25 can be factored into 5^2, and since they do not share any common factors other than 1, the greatest common factor is 1.

Well, honey, the factor for 24ab is 1, 2, 3, 4, 6, 8, 12, 24, a, b, 2a, 3a, 4a, 6a, 8a, 12a, 24a, b, 2b, 3b, 4b, 6b, 8b, 12b, and 24b. So, you've got plenty of options to choose from, darlin'. Just pick your poison and factor away!

The prime factors of 78 are 2, 3, and 13. To find the prime factors of a number, you can start by dividing the number by the smallest prime number, which is 2. If the number is divisible by 2, continue dividing by 2 until you reach a point where it is no longer divisible by 2. Then, move on to the next prime number, which is 3. Repeat the process until you have factored the number completely into its prime factors.

To find the greatest common factor (GCF) of 15, 24, and 30, we first need to find the factors of each number. The factors of 15 are 1, 3, 5, and 15. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The GCF of 15, 24, and 30 is the largest number that is a factor of all three numbers, which in this case is 3.

To determine if the first number is divisible by the second, you need to divide the first number by the second number. If the division result is a whole number without a remainder, then the first number is divisible by the second. For example, if the first number is 12 and the second number is 3, when you divide 12 by 3, the result is 4, which is a whole number, indicating that 12 is divisible by 3.

No, 2x2x5 is not a prime factorization because 2 is not a prime factor. A prime factorization is a representation of a number as a product of prime numbers. In this case, the prime factorization of 2x2x5 would be 2x2x5 or 2^2x5.

Well, honey, there are plenty of ways to make 235. You could add 200 and 35, or subtract 765 from it. Shoot, you could even multiply 47 by 5 to get there. The possibilities are endless, just like my love for a good martini.

Well, isn't that a happy little math question! Let's find the factors of 250 and 375. The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250. The factors of 375 are 1, 3, 5, 15, 25, 75, 125, and 375. The highest common factor they share is 25. Just like painting, math can be a beautiful blend of patterns and numbers coming together harmoniously.

The index notation of 294 is 2 x 3^5, where 2 is the base and 5 is the exponent. This means that 294 can be expressed as the product of 2 and 3 raised to the power of 5. In index notation, the number is broken down into its prime factors and expressed as a product of primes with corresponding exponents.

To find the Least Common Multiple (LCM) of 9, 16, and 25, we first need to prime factorize each number.

9 = 3^2, 16 = 2^4, and 25 = 5^2.

Then, we take the highest power of each prime factor that appears in any of the numbers: 2^4 * 3^2 * 5^2 = 400.

Therefore, the LCM of 9, 16, and 25 is 400.

To find the least common multiple (LCM) of a set of numbers, you need to first find the prime factorization of each number. Then, you take the highest power of each prime factor that appears in any of the factorizations. In this case, the prime factorization of each number is: 2, 3, 2^2, 5, 2 * 3, 7, 2^3, 3^2, 2 * 5, 11, 2^2 * 3. Taking the highest power of each prime factor, the LCM is 2^3 * 3^2 * 5 * 7 * 11 = 27720.

1, 59

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

1, 61

1, 2, 31, 62

1, 3, 7, 9, 21, 63

1, 2, 4, 8, 16, 32, 64

1, 5, 13, 65

1, 2, 3, 6, 11, 22, 33, 66

1, 67

1, 2, 4, 17, 34, 68

1, 3, 23, 69

The prime factors of 165 are 3, 5, and 11. To find the prime factors of 165, we start by dividing 165 by the smallest prime number, which is 3. This gives us 55. Then, we continue dividing by prime numbers until we can no longer divide evenly, resulting in the prime factors of 3, 5, and 11.

The factors of 8624 are the numbers that can be multiplied together to give the original number. The factors of 8624 are 1, 2, 4, 8, 17, 34, 68, 136, 59, 118, 236, 472, 1009, 2018, 4036, and 8072. The prime factors of 8624 are the prime numbers that can be multiplied together to give the original number. The prime factors of 8624 are 2, 17, 59, and 1009.

Oh, dude, non-trivial factors are basically any factors that are not trivial. Trivial factors are like the boring, basic ones that don't really matter much, you know? So, non-trivial factors are the ones that actually have some significance or impact on the situation. It's like the cool kids at the party versus the wallflowers.

I think one or both of those have to be negative.

-3 + 7 = 4

-3 x 7 = -21

3 + -7 = -4

3 x -7 = -21

7 x 3 = 21

7 - 3 = 4

It also works if you subtract.

Well, darling, the Highest Common Factor (HCF) of 50 and 90 is 10. It's like finding the hottest person at a party - they gotta be able to divide both 50 and 90 without leaving a remainder. So, 10 is the lucky number that fits the bill.

1000 x 1000

The Highest Common Factor (HCF) of 210 and 165 is the largest positive integer that divides both numbers without leaving a remainder. To find the HCF, you can use the Euclidean algorithm, which involves dividing the larger number by the smaller number and then using the remainder as the new divisor until the remainder becomes zero. In this case, the HCF of 210 and 165 is 15.

To find the sum of the first 4 multiples of 6, you can use the formula for the sum of an arithmetic series: Sn = n/2 * (a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term. In this case, the first 4 multiples of 6 are 6, 12, 18, and 24. Plugging these values into the formula, you get Sn = 4/2 * (6 + 24) = 2 * 30 = 60. Therefore, the sum of the first 4 multiples of 6 is 60.

The two numbers between 35 and 46 that are the greatest common factors are 41 and 43. To determine the greatest common factor of two numbers, you need to find the largest number that divides both numbers evenly. In this case, 41 and 43 are both prime numbers and have no common factors other than 1, making them the greatest common factors between 35 and 46.

1 x 78, 2 x 39, 3 x 26, 6 x 13.

Oh, dude, you're hitting me with some math now! So, like, if you want to know what times what equals 162, you're basically asking for the factors of 162. It's like 2 times 81, or 6 times 27, or even 9 times 18. It's all good, man, just some basic multiplication vibes.

Yes.

Oh, dude, common factors for 16 and 24? Let's see, like, 1, 2, 4, and 8 are all factors they have in common. So, if you're looking for numbers that can divide both 16 and 24 without leaving a remainder, those are your go-to options. Math can be chill sometimes, you know?