Factoring and Multiples

Oh, dude, the Highest Common Factor (HCF) of 294 and 252 is 42. It's like the number that you can divide both of them by without any remainders. So yeah, 42 is the magical number that's the biggest factor they both have in common. Cool, right?

Step 1: Express each number as product of prime factors

7 = 1 * 7

8 = 2 * 2 * 2

10 = 2 * 5

Step 2: Pick up distinct numbers from each set and multiply them

7 * 2 * 2 * 2 * 5 = 280

Remember that when we talk about per cent, we mean, "parts of a hundred". So when we mean "all of something", we can say, 100%. 600% will be 6 * 100%, in other words, 6 times something. So 2 inches times 600% will equal 2 * 6, or 12. The way to convert a percentage to a fraction is to multiply it by 100. So 600% equals 600/100, which equals 6/1, which in turn equals 6.

Every number with a factor of 10 must have factors of 2 and 5. This is because 10 can be expressed as 2 x 5. Any number that is a multiple of 10 will have both 2 and 5 as factors, along with any other factors it may have. These two prime factors are essential for a number to have a factor of 10.

There is nothing to factor. x - 1 is already in its lowest terms.

To find the greatest common factor (GCF) of 12, 60, and 68, we first need to find the prime factorization of each number. The prime factorization of 12 is 2^2 * 3, the prime factorization of 60 is 2^2 * 3 * 5, and the prime factorization of 68 is 2^2 * 17. The GCF is the product of the common prime factors raised to the lowest power, which in this case is 2^2 = 4. Therefore, the greatest common factor of 12, 60, and 68 is 4.

To find the greatest common factor (GCF) of 264 and 660, we first need to list the factors of each number. The factors of 264 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 88, 132, and 264. The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, and 660. The GCF of 264 and 660 is the largest number that appears in both lists, which is 132.

Oh, what a lovely question! To find the greatest common factor of 27, 54, and 108, we can first list the factors of each number. The factors of 27 are 1, 3, 9, and 27. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Lastly, the factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108. The greatest common factor shared by all three numbers is 27.

3 and 9 both work

They are 90, 180, 270, 360, and 450.

The highest common factor (HCF) of 10 and 25 is 5. This is because 5 is the largest positive integer that divides both 10 and 25 without leaving a remainder. The factors of 10 are 1, 2, 5, and 10, while the factors of 25 are 1, 5, 25. The highest common factor is the greatest number that appears in both lists, which in this case is 5.

To find the least common multiple (LCM) of 18, 24, and 30, we first need to find the prime factorization of each number.

18 = 2 * 3^2 24 = 2^3 * 3 30 = 2 * 3 * 5

Next, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3^2 * 5 = 360.

Therefore, the least common multiple of 18, 24, and 30 is 360.

Oh honey, let me break it down for you. The multiples of 3 between 200 and 300 are 201, 204, 207, 210, 213, 216, 219, 222, 225, 228, 231, 234, 237, 240, 243, 246, 249, 252, 255, 258, 261, 264, 267, 270, 273, 276, 279, 282, 285, 288, 291, 294, 297. You're welcome!

In the context of driving, the term "litters" typically refers to fuel consumption, specifically in liters per hour (L/hr). The amount of fuel consumed during one hour of driving can vary significantly depending on the vehicle's fuel efficiency, engine size, driving conditions, and speed. On average, a car may consume anywhere from 5 to 15 liters of fuel per hour, with larger vehicles such as trucks or SUVs potentially consuming more. To determine the exact amount of fuel consumed in one hour of driving, it is necessary to know the specific fuel consumption rate of the vehicle in question.

If you keep doubling the total, at the end of one day you'd have two cents. At the end of the first week, you'd have $1.28. At the end of 100 days, you'd be wealthy beyond your wildest dreams. If you keep doubling the same penny, at the end of 100 days you'd have a couple bucks.

Well, isn't that just a happy little question! To find the greatest common factor (GCF) of 24, 40, and 64, we can start by listing the factors of each number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. Lastly, the factors of 64 are 1, 2, 4, 8, 16, 32, and 64. After comparing these lists, we see that the greatest common factor of 24, 40, and 64 is 8. Isn't that just a happy little number to find?

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 210, 213, 216, 219, 222, 225, 228, 231, 234, 237, 240, 243, 246, 249, 252, 255, 258, 261, 264, 267, 270, 273, 276, 279, 282, 285, 288, 291, 294, 297, 300, 303, 306, 309, 312, 315, 318, 321, 324, 327, 330, 333, 336, 339, 342, 345, 348, 351, 354, 357, 360, 363, 366, 369, 372, 375, 378, 381, 384, 387, 390, 393, 396, 399, 402, 405, 408, 411, 414, 417, 420, 423, 426, 429, 432, 435, 438, 441, 444, 447, 450, 453, 456, 459, 462, 465, 468, 471, 474, 477, 480, 483, 486, 489, 492, 495, 498, 501, 504, 507, 510, 513, 516, 519, 522, 525, 528, 531, 534, 537, 540, 543, 546, 549, 552, 555, 558, 561, 564, 567, 570, 573, 576, 579, 582, 585, 588, 591, 594, 597, 600, 603, 606, 609, 612, 615, 618, 621, 624, 627, 630, 633, 636, 639, 642, 645, 648, 651, 654, 657, 660, 663, 666, 669, 672, 675, 678, 681, 684, 687, 690, 693, 696, 699, 702, 705, 708, 711, 714, 717, 720, 723, 726, 729, 732, 735, 738, 741, 744, 747, 750, 753, 756, 759, 762, 765, 768, 771, 774, 777, 780, 783, 786, 789, 792, 795, 798, 801, 804, 807, 810, 813, 816, 819, 822, 825, 828, 831, 834, 837, 840, 843, 846, 849, 852, 855, 858, 861, 864, 867, 870, 873, 876, 879, 882, 885, 888, 891, 894, 897, 900, 903, 906, 909, 912, 915, 918, 921, 924, 927, 930, 933, 936, 939, 942, 945, 948, 951, 954, 957, 960, 963, 966, 969, 972, 975, 978, 981, 984, 987, 990, 993, 996, 999.

The prime factorization of 1512 is 2^3 * 3^3 * 7. This means that 1512 can be expressed as the product of these prime numbers raised to their respective powers. The prime factorization helps us understand the unique combination of prime numbers that make up the original number.

Well, honey, the Least Common Multiple (LCM) of 18, 81, and 270 is 810. It's like finding the common ground in a messy family reunion - you gotta pick the biggest number that all the others can agree on. So, there you have it, 810 is the magic number that keeps these three troublemakers in line.

1 x 320, 2 x 160, 4 x 80, 5 x 64, 8 x 40, 10 x 32, 16 x 20.

The pattern in the sequence is multiplying the previous number by a factor that increases by 2 each time. Starting with 2, the next number is obtained by multiplying 2 by 2 (to get 4), then by 3 (to get 12), then by 4 (to get 48), and finally by 5 (to get 240). Therefore, the next number in the sequence would be 240 multiplied by 6, which equals 1440.

The highest common factor of 119 and 161 is seven. You have to find all of the numbers factors before you can work it out. the factors of 119 are 1,7,17 and 119, and the factors of 161 are 1,7,23 and 161, therefore the only number that occurs twice in both sequences is 7 so that is the highest common factor

Oh, dude, you're hitting me with the prime factorization question? Like, chill out, man. The number with prime factors of 2, 3, and 5 is 30. It's like the cool kid at the prime factor party, hanging out with all the popular primes.

The greatest common factor of 4xy and -6xy is 2xy. To find the greatest common factor, we first factor out the numbers 4 and -6 to get 2(2xy) and -2(3xy). The greatest common factor is the highest common factor that divides both terms evenly, which in this case is 2xy.

The greatest common factor (GCF) of 16x and 36x is 4x. To find the GCF, you need to identify the common factors of both numbers. In this case, both 16 and 36 share a common factor of 4. Additionally, both terms have a common variable factor of x. Therefore, the GCF is 4x.