Factoring and Multiples

The sequence appears to be increasing at a variable rate. The pattern seems to be adding 1, then 3, then 5, then 10. Following this pattern, the next number in the sequence would be 20 + 15, which equals 35.

To find a pair of numbers with a least common multiple of 20 and a greatest common factor of 2, we need to consider the prime factorization of 20, which is 2^2 * 5. The greatest common factor of 2 means that the two numbers must have a common factor of 2. Therefore, a pair of numbers that satisfies these conditions is 4 and 10, as their least common multiple is 20 (2^2 * 5) and their greatest common factor is 2.

The factors of a number are the integers that can be multiplied together to result in that number. For numbers 1 to 200, the factors will vary depending on the number itself. For example, the factors of 1 are 1, while the factors of a prime number like 2 are only 1 and 2. The factors of a composite number like 12 are 1, 2, 3, 4, 6, and 12. To find all the factors of each number from 1 to 200, you would need to perform factorization for each individual number.

The GCF is 9.

In the number 36, the digit 3 is in the tens place. This means that the value of the digit 3 is actually 30, as it represents 3 tens or 3 groups of 10. The value of a digit in a number is determined by its position in the number relative to the place value system, where each place represents a power of 10.

Well, isn't that just a happy little question! To find the LCM of 84 and 360 using prime factorization, we first break down each number into its prime factors. For 84, that's 2^2 * 3 * 7, and for 360, it's 2^3 * 3^2 * 5. Then, we take the highest power of each prime factor that appears in either number, which gives us 2^3 * 3^2 * 5 * 7, resulting in an LCM of 2,520.

Well, honey, 4950 is divisible by 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450, and of course, itself. So, there you have it, a whole bunch of divisors for your mathematical enjoyment.

Well, darling, the estimate of 512 is around 500. I mean, it's not rocket science, just round that bad boy to the nearest hundred and call it a day. Math doesn't have to be a headache, honey.

Well, honey, 178 can be divided by 1, 2, 89, and 178 itself. That's it, no more, no less. So, if you were hoping for some exciting divisors, I'm sorry to disappoint. But hey, at least you know the facts now.

To find the common factors of 8 and 12, we first list the factors of each number. The factors of 8 are 1, 2, 4, and 8, while the factors of 12 are 1, 2, 3, 4, 6, and 12. The common factors are 1, 2, and 4. To find the sum of these common factors, we add them together: 1 + 2 + 4 = 7. So, the sum of all the common factors of 8 and 12 is 7.

Oh, dude, you're hitting me with the math questions! Alright, so 84 cubed is 592,704. To break it down into prime factors, you'd be like, "Hey, 2, 3, and 7, what's up?" And they'd be like, "We're the prime factors of 592,704, bro." So, in index form, it would be 2^6 x 3^3 x 7^2. Easy peasy, lemon squeezy!

5^2

If you're not afraid of working with fractions or decimals, then there are an infinite number of

possibilities. Even if you only want to talk about positive whole numbers, and you can only handle

two of them at a time, there are still several possibilities:

1 x 375

3 x 125

5 x 75

15 x 25 .

Oh, dude, the greatest common factor is the largest number that divides evenly into both 12 and 18, which in this case is 6. The least common multiple, on the other hand, is the smallest multiple that both 12 and 18 share, which in this case is 36. So, like, one's about sharing factors and the other's about sharing multiples, you know?

To find the numbers that multiply to get 1680, we need to factorize 1680. The prime factorization of 1680 is 2^4 * 3 * 5 * 7. Therefore, the numbers that multiply to get 1680 are 2, 2, 2, 2, 3, 5, and 7.

Oh, dude, math time! So, if 3 1/2 bags of seed cost $35, then each bag costs $10. Now, if you want to know what 4 1/2 bags will cost, just add another $10 for the extra bag. So, 4 1/2 bags will cost $45. Easy peasy, lemon squeezy!

Well, honey, the multiples of five up to 2000 are 5, 10, 15, 20, and so on all the way up to 2000. It's like counting by fives, but with a bit more sass. So, buckle up and start counting those multiples like a boss!

Oh, dude, let me break it down for you. So, from least to greatest, it goes like this: -8, -5, 0, 3, 4. Easy peasy lemon squeezy. Hope that helps!

The multiples of 16 are 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 272, 288, 304, 320, 336, 352, 368, 384, 400, 416, 432, 448, 464, 480, 496, 512, 528, 544, 560, 576, 592, 608, 624, 640, 656, 672, 688, 704, 720, 736, 752, 768, 784, 800, 816, 832, 848, 864, 880, 896, 912, 928, 844, 960, 976, 992, 1008... There is an infinite number of them.
16, 32, 48 and so on.
16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,etc etc

Well, isn't that a happy little math question! The greatest common factor (GCF) of 100 and 300 is 100 because it's the largest number that divides evenly into both 100 and 300. Just like adding a touch of alizarin crimson to highlight a mountain, finding the GCF can help us simplify things and see the beauty in numbers.

To write 49 over 72 in simplest form, you need to find the greatest common factor (GCF) of 49 and 72, which is 1. Divide both the numerator and denominator by the GCF to simplify the fraction. Therefore, 49/72 in simplest form is 49/72.

The Least Common Multiple (LCM) of 4, 5, and 12 is the smallest multiple that all three numbers share. To find the LCM, you need to first find the prime factorization of each number: 4 = 2^2, 5 = 5^1, and 12 = 2^2 * 3^1. Then, you take the highest power of each prime factor that appears in any of the numbers: 2^2 * 3^1 * 5^1 = 60. Therefore, the LCM of 4, 5, and 12 is 60.

Well, darling, number 19 is as prime as a fine wine. It can't be divided by anything other than 1 and itself, making it a prime number. So, rest easy knowing that 19 is standing strong in the prime club, not messing around with any composite nonsense.

The two numbers that add to give you 18 and multiply to give you 40 are 10 and 8. This is because 10 + 8 = 18 and 10 x 8 = 80. However, if the question is referring to two numbers that add to 18 and multiply to 40, the correct pair would be 5 and 8, as 5 + 8 = 13 and 5 x 8 = 40.

Well, honey, technically speaking, 2.4 and 2.40 are the same number. One just likes to dress up with an extra zero to feel fancy. But at the end of the day, they both represent the exact same value, so no need to make a big fuss about it.