Factoring and Multiples

To find the greatest common factor (GCF) of 52, 156, and 169, we need to first factor each number. The factors of 52 are 1, 2, 4, 13, 26, and 52. The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, and 156. The factors of 169 are 1, 13, and 169. The GCF is the largest number that is a factor of all three numbers, which in this case is 13.

To find the Highest Common Factor (HCF) of 35, 77, and 91, you need to factorize each number. The factors of 35 are 1, 5, 7, 35. The factors of 77 are 1, 7, 11, 77. The factors of 91 are 1, 7, 13, 91. The common factor among these three numbers is 7, so the HCF of 35, 77, and 91 is 7.

The highest common factor of 112 qnd 392 is 56

Sure thing, honey. 20 million 5 hundred thousand in expanded notation using exponents is 2 x 10^7 + 5 x 10^5. Just break down the numbers and slap those exponents on 'em like it's nobody's business. Easy peasy lemon squeezy.

To find the Greatest Common Factor (GCF) of 78, 168, and 486, we first need to find the prime factorization of each number.

78 = 2 * 3 * 13 168 = 2^3 * 3 * 7 486 = 2 * 3^5

Next, we identify the common prime factors among the three numbers, which are 2 and 3. The GCF is the product of these common prime factors raised to the lowest power they appear in any of the numbers. Therefore, the GCF of 78, 168, and 486 is 2 * 3 = 6.

The numbers that go into 35 are 1, 5, 7, and 35. The numbers that go into 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.

Oh, dude, multiples of 23 to 100? Okay, let me casually drop some knowledge on you. So, the multiples of 23 up to 100 are 23, 46, 69, and 92. It's like counting by 23s, but stopping before you hit 100. Easy peasy!

Oh, dude, let me break out the ol' calculator for this brain-buster. So, like, 144 divided by 8 equals 18. So, 8 can go into 144 a cool 18 times. Math is wild, man.

2 is a factor of 18 and is not a multiple of 3.

The greatest common factor or the highest common factor is the highest number that divides exactly into two or more numbers.

24: 1, 2, 3, 4, 6, 8, 12, 24

30: 1, 2, 3, 5, 6, 10, 15, 30

The GCF of 24 and 30 is 6.

111

The prime factors of 392 are 2, 2, 2, 7, and 7. To find the prime factors, you divide 392 by the smallest prime number (2) until you cannot divide evenly. The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, and 392. These are all the numbers that can divide evenly into 392.

Well, let's think of the Highest Common Factor (HCF) like a happy little friend that both numbers can share. To find it, we look for the largest number that can divide both 200 and 175 evenly. In this case, the HCF of 200 and 175 is 25. Just like in painting, finding the HCF is all about seeing the beauty in the numbers coming together harmoniously.

The factor pairs of 72 are pairs of numbers that can be multiplied together to give the number 72. The factor pairs of 72 are (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9). These pairs represent all the combinations of numbers that, when multiplied, result in 72.

48000 can be expressed as the product of its prime factors, which are 2^6 * 3 * 5^3. It can also be written as 2^6 * 3 * 5^3 in exponential form. In terms of factors, 48000 can be divided evenly by 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 320, 480, 800, 960, 1200, 2400, and 4800.

The value must be '5' or more. e.g. 6, 7. et seq.,

13 is prime

14=2x7, 2 factors

15=3x5, 2 factors

16=24, 4 factors

17 is prime

18=2x32, 3 factors

19 is prime

So the answer is 3 (14, 15 and 16)

To make 27 using the numbers 1, 2, 3, and 4 only once, you can use the following mathematical expression: (3 * 4) + (2 * 1) = 12 + 2 + 1 = 27. This equation follows the order of operations (multiplication before addition) to correctly arrive at the desired result of 27.

To express 0.835 as a fraction, we can write it as 835/1000. This is because the decimal 0.835 can be represented as 835 thousandths. To simplify this fraction, we can divide both the numerator and the denominator by 5, resulting in the simplified fraction 167/200. Therefore, 0.835 is equivalent to the fraction 167/200.

Well, darling, 34 is snug as a bug between the multiples of 10, specifically 30 and 40. So, it's not quite cozy with the 10s, but it's definitely hanging out in the neighborhood.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are the prime numbers in this range, and there are 25 of them. So, of the 100 numbers, 25 are pime, giving us 25%.

Oh honey, the Greatest Common Factor (GCF) of 72, 144, and 192 is 24. It's like finding the common ground between three friends who all love pizza but can't agree on toppings. So, 24 is the magical number that can divide all three of these numbers without any drama.

Well, honey, if you paid attention in math class, you'd know that yes, all multiples of 6 are also multiples of 12. Why? Because 12 is a multiple of 6, so any number that is a multiple of 6 will also be a multiple of 12. It's simple math, darling.

Oh, isn't that a happy little question? To find the Least Common Multiple (LCM) of 35, 65, and 90, we can start by listing the prime factors of each number. Then, we can take the highest power of each prime factor that appears in any of the numbers. By doing this, we find the LCM, which is like a beautiful harmony of these numbers coming together. Just like how different colors blend on a canvas to create a masterpiece!

Oh, dude, the greatest common factor of 84, 154, and 168 is 14. It's like the superhero that swoops in and saves the day by being the largest number that can divide all three of those numbers evenly. So yeah, 14 is the real MVP in this math problem.