Factoring and Multiples

The least common multiple (LCM) of two numbers is the smallest multiple that is divisible by both numbers. In this case, the LCM of 7 and 49 is 49 because it is the smallest multiple of 7 that is also a multiple of 49. This is because 49 is a multiple of 7 (7 x 7 = 49), so it is the smallest number that satisfies both conditions.

Oh, that's a happy little math question! To find the highest common factor of 120 and 405, we can first list the factors of each number. For 120, the factors are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120. For 405, the factors are 1, 3, 5, 9, 15, 27, 45, 81, and 405. The highest common factor is 15, which is the largest number that both 120 and 405 can be divided by evenly.

Well, honey, if you're looking to crack the code of 34, you're gonna need to multiply 1 by 34 or 2 by 17. That's the tea, darling. So, take your pick and go forth with your newfound mathematical wisdom.

The prime factorization of 110 is 2 x 5 x 11. The product of these prime factors is calculated by multiplying them together: 2 x 5 x 11 = 110. So, the product of the prime factors of 110 is 110.

Oh, dude, you want me to do math? Alright, let me dust off my calculator. So, the LCM of 3 and 8 is 24, right? Cool. The next four common multiples after that are 24, 48, 72, and 96. Boom, math wizard strikes again!

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.

Oh, dude, the greatest common factor of 720? That's like the biggest number that can divide into 720 without leaving a remainder. So, let's see, the factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, and so on. The greatest one that they all have in common is like the biggest, baddest factor they can all agree on. And that's 360!

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

12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444, 456, 468, 480, 492, 504, 516, 528, 540, 552, 564, 576, 588, 600, 612, 624, 636, 648, 660, 672, 684, 696, 708, 720, 732, 744, 756, 768, 780, 792, 804, 816, 828, 840, 852, 864, 876, 888, 900, 912, 924, 936, 948, 960, 972, 984, 996.

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.