Factoring and Multiples

210, 330, 390, 420 and 462

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, and so on.

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, and so on.

The common multiples of 3 and 4 would be 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132...

Oh, dude, the greatest common factor of those numbers is like the biggest number that can divide all of them evenly. So, like, the GCF of 12, 16, 20, and 24 is 4 because it's the largest number that can go into each of those numbers without leaving a remainder. Math can be cool, man.

The greatest common factor (GCF) of 720 is the largest positive integer that divides evenly into 720. To find the GCF, you need to factorize 720 into its prime factors, which are 2^4 x 3^2 x 5. The GCF is the product of the common prime factors raised to the lowest power they appear in the factorization, which in this case is 2^3 x 3^1 x 5^0 = 24. Therefore, the greatest common factor of 720 is 24.

The prime factorization of 14 in exponential form is 21x71.

Oh honey, the least common multiple of 2, 5, and 12 is 60. That's the smallest number that all three of those divas can divide into without any drama. So, go ahead and party like it's 1960 with that LCM!

Oh, dude, factors are like friends who divide a number without any drama. So, for 25, you've got 1, 5, and 25 hanging out, keeping it simple. And for 75, it's 1, 3, 5, 15, 25, and 75 all in the mix. Just a chill math party, you know?

There is no easy way. You can keep dividing the number by 2 but then you could be left with a large number which may be the product of two very large primes. There is no simple way to find the factors of such a composite number, and that is why they are used for data encryption.

Well, honey, the highest common factor of 405 and 720 is 45. It's like finding the biggest slice of cake you can share between those two numbers - in this case, it's a slice of 45. So, there you have it, 45 is the boss when it comes to dividing up 405 and 720.

The common factors of 9 and 7 are the numbers that can evenly divide both 9 and 7 without leaving a remainder. In this case, the only common factor of 9 and 7 is 1, as 9 is a prime number and only has 1 and itself as factors. Therefore, the common factors of 9 and 7 are 1.

7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119, 126, 133, 140, 147, 154, 161, 168, 175, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 287, 294.

The solution to the given problem can be obtained by sum formula of arithmetic progression.

In arithmetic progression difference of two consecutive terms is constant. The multiples of any whole number(in sequence) form an arithmetic progression.

The first multiple of 3 is 3 and the 100th multiple is 300.

3, 6, 9, 12,... 300. There are 100 terms.

The sum 3 + 6 + 9 + 12 + ... + 300 can be obtained by applying by sum formula for arithmetic progression.

Sum = (N/2)(First term + Last term)

where N is number of terms which in this case is 100.

First term = 3; Last term = 300.

Sum = (100/2)(3 + 300) = 50 x 303 = 15150.

The common multiples of 6, 7, and 8 are numbers that are divisible by all three of these numbers. To find the common multiples, we first list the multiples of each number: 6 (6, 12, 18, 24, 30, ...), 7 (7, 14, 21, 28, 35, ...), and 8 (8, 16, 24, 32, 40, ...). The common multiples of 6, 7, and 8 are the numbers that appear in all three lists, such as 24 and 48.

Well, isn't that just a happy little question! Numbers that end with 0 or 5 are multiples of 5. So, 5 itself is a factor that ends with 0 or 5, along with numbers like 10, 15, 20, and so on. Just imagine those numbers as colorful dots on your canvas, adding a lovely touch to your mathematical masterpiece.

1, 2, 4, 5, 8, 10, 17, 20, 25, 34, 40, 50, 68, 85, 100, 136, 170, 200, 340, 425, 680, 850, 1700, 3400.

The highest common factor (HCF) and least common multiple (LCM) are used in daily life for various practical applications, such as simplifying fractions, calculating time intervals, and organizing schedules. For example, when baking or cooking, HCF and LCM can help determine the right proportions of ingredients or cooking times for multiple dishes. In logistics, LCM can be used to schedule deliveries or plan routes efficiently. Understanding HCF and LCM can streamline decision-making processes and optimize resource allocation in everyday tasks.

9 divided by 6 is one and one half so the answer is one and one half times.

The GCF is 14.

The factors of 32 are 1, 2, 4, 8, 16, and 32. The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. Factors are numbers that can be multiplied together to get the original number.

Multiples of 15 are numbers that can be divided evenly by 15 without leaving a remainder. To find the multiples of 15, you can simply multiply 15 by all the natural numbers (1, 2, 3, 4, etc.). The first few multiples of 15 are 15, 30, 45, 60, 75, and so on. These numbers follow a pattern where each multiple is obtained by adding 15 to the previous multiple.

Well, isn't that a happy little question! If you take 450 and divide it by 5, you'll find that it goes in 90 times. Just imagine each time you divide, it's like painting a beautiful landscape with numbers. Happy dividing, my friend!

The greatest common factor (GCF) of 14 and 16 is 2. To find the GCF, you need to determine the factors of each number. The factors of 14 are 1, 2, 7, and 14, while the factors of 16 are 1, 2, 4, 8, and 16. The largest number that appears in both lists is 2, making it the greatest common factor.

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCF of 45 and 100, you need to determine the common factors of both numbers. The factors of 45 are 1, 3, 5, 9, 15, and 45, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The greatest common factor of 45 and 100 is 5, as it is the largest number that is a factor of both 45 and 100.

Numbers with exactly 6 factors are called highly composite numbers. These numbers have a total of 6 factors, including 1 and the number itself. Highly composite numbers are typically of the form p^2 * q, where p and q are prime numbers. Examples of numbers with 6 factors include 12 (2^2 * 3) and 24 (2^3 * 3).

Oh, dude, you're hitting me with some math vibes here! The highest common factor of 14, 36, and 175 is like the cool kid at the party - it's the biggest number that can divide all of them without any leftovers. So, the HCF of these numbers is 1 because they don't have any common factors other than 1. Math can be chill too, you know?