Factoring and Multiples

To create a factor rainbow for the number 72, you would first identify all the factors of 72. The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. To create the factor rainbow, you would typically arrange these factors in a way that shows their relationships, such as in a visual diagram with lines connecting related factors. This can help visualize the prime factorization of 72 as well as how the factors are interconnected.

Well, honey, 104 is a multiple of 13 because 104 divided by 13 equals 8 with no remainder. However, it's not a multiple of 14 because when you divide 104 by 14, you get 7 with a remainder of 6. So, in short, 104 is only a multiple of 13, not 14. Hope that clears things up for ya!

Oh, dude, it's like super easy! So, first you can factor out the greatest common factor, which is 7. Then you're left with x - 9. And that's it! You've factored 7x - 63 into 7(x - 9). Easy peasy lemon squeezy!

The greatest common factor (GCF) of 120 and 200 is 40. To find the GCF, you need to determine the factors of each number and then identify the largest number that is a factor of both. The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200. The largest number that appears in both lists is 40, making it the greatest common factor.

The first ten multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. Multiples are numbers that can be divided evenly by a given number, in this case, 3. Each subsequent multiple is found by adding 3 to the previous multiple.

The least common multiple of 3, 7, and 11 is 231.

To find the greatest common factor of 260 and 195, we need to find the factors of each number. The factors of 260 are 1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, and 260. The factors of 195 are 1, 3, 5, 13, 15, 39, 65, and 195. The greatest common factor of 260 and 195 is 65, as it is the largest number that divides both 260 and 195 without leaving a remainder.

Well, isn't that just a happy little math question? The highest common factor of 12 and 42 is 6. You see, the highest common factor is the largest number that can divide evenly into both 12 and 42, and in this case, that number is 6. Just like adding a touch of titanium white to your painting, finding the highest common factor can bring clarity and harmony to your math problems.

The number 44 can be divided evenly by 1, 2, 4, 11, 22, and 44. These numbers are factors of 44 because they divide evenly into 44 without leaving a remainder. Factors are numbers that can be multiplied together to get the original number, in this case, 44.

To find the greatest common factor (GCF) of 24, 42, and 48, we first need to find the factors of each number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The GCF of 24, 42, and 48 is 6, as it is the largest number that divides all three numbers without leaving a remainder.

The lowest common factor of two numbers is the smallest positive integer that both numbers can be divided by without leaving a remainder. In this case, the factors of 3 are 1 and 3, while the factors of 4 are 1, 2, and 4. The lowest common factor of 3 and 4 is 1, as it is the only factor that both numbers share.

21/24 and 20/24

1, 2, 4 and 8 are their only common factors.

Oh, dude, of course! A composite number is just a number that can be broken down into smaller numbers, like a Lego set. And prime factors are the prime numbers that multiply together to give you that composite number. So, like, yeah, you can totally factor a composite number into prime factors. It's like breaking down a complicated recipe into its basic ingredients.

Well, isn't that just a happy little fraction we have here! To simplify 8 over 20, we can divide the top and bottom by 4 since they both have a common factor. So, 8 divided by 4 is 2, and 20 divided by 4 is 5. Therefore, 8 over 20 simplifies to 2 over 5. Just like that, we've created a beautiful, simplified fraction!

Oh, dude, the least common multiple of 22 and 48 is 264. It's like when you're trying to find a parking spot at the mall during the holidays - you gotta drive around a bit to find the perfect fit. So, 264 is the magical number where both 22 and 48 can peacefully coexist without any drama.

The number 4 divides exactly into 16. This is because 16 divided by 4 equals 4, with no remainder. In general, a number divides exactly into another number if the division results in a whole number quotient without any remainder.

Oh, dude, multiples of 13 up to 1000? Like, you just want me to list them all out for you? Okay, fine, here we go: 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 156, 169, 182, 195, 208, 221, 234, 247, 260, 273, 286, 299, 312, 325, 338, 351, 364, 377, 390, 403, 416, 429, 442, 455, 468, 481, 494, 507, 520, 533, 546, 559, 572, 585, 598, 611, 624, 637, 650, 663, 676, 689, 702, 715, 728, 741, 754, 767, 780, 793, 806, 819, 832, 845, 858, 871, 884, 897, 910, 923, 936, 949, 962, 975, 988. Done.

The Least Common Multiple (LCM) of 100 and 180 can be found by first determining the prime factorization of each number. The prime factors of 100 are 2^2 * 5^2, and the prime factors of 180 are 2^2 * 3^2 * 5. To find the LCM, we take the highest power of each prime factor that appears in either number, which gives us 2^2 * 3^2 * 5^2 = 900. Therefore, the LCM of 100 and 180 is 900.

A common factor of 32, 64, and 76 is a number that divides evenly into all three of these numbers. To find the common factors, we can first find the prime factorization of each number. The prime factorization of 32 is 2^5, the prime factorization of 64 is 2^6, and the prime factorization of 76 is 2^2 * 19. The common factor among these three numbers is 2^2, which is 4.

Prime factorization is the finding which prime number multiply to get to make the original number.

Factors of 75: 1, 3, 5, 15, 25, 75

Prime factors: 3, 5

3 x 5 x 5 = 75

Ah, the Highest Common Factor, isn't that a happy little concept? Let's see, to find the HCF of 260, we can break it down into its prime factors, which are 2 x 2 x 5 x 13. Then, we look for the common factors it shares with other numbers to find the highest one. Remember, there are no mistakes, just happy little accidents in mathematics!