Factoring and Multiples

To find the least common multiple (LCM) of 48, 84, and 144, we first need to find the prime factorization of each number.

48 = 2^4 * 3 84 = 2^2 * 3 * 7 144 = 2^4 * 3^2

Next, we take the highest power of each prime factor that appears in any of the numbers: 2^4, 3^2, 7.

Multiplying these together, we get LCM(48, 84, 144) = 2^4 * 3^2 * 7 = 2016.

Therefore, the least common multiple of 48, 84, and 144 is 2016.

To find the highest common factor (HCF) of 16 and 24, we first list the factors of each number. The factors of 16 are 1, 2, 4, 8, and 16. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The highest common factor is the largest number that both lists share, which is 8. Therefore, the HCF of 16 and 24 is 8.

Oh, dude, the smallest number with 4 different prime factors is 2 x 3 x 5 x 7, which equals 210. It's like the VIP of numbers, all exclusive with its different prime factor squad. So yeah, that's the answer, no biggie.

To compare 0.6 and 2/3, we need to convert 0.6 to a fraction. 0.6 can be written as 6/10 or simplified to 3/5. Now we can compare 3/5 and 2/3. To do this, we need to find a common denominator, which is 15 in this case. Multiplying 3/5 by 3/3 gives us 9/15 and multiplying 2/3 by 5/5 gives us 10/15. Therefore, 2/3 is greater than 0.6.

The Greatest Common Factor (GCF) of 84, 63, and 42 is 21.

The greatest common factor is either the difference between the numbers or a factor of the difference between the numbers.

Note: 84 - 63 = 21 and 63 - 42 = 21. So, the greatest common factor might be 21.

When you divide each of the numbers by 21, it divides evenly, so 21 is the greatest common factor.

Another way to determine the greatest common factor is to find all the factors of the numbers and compare them.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.

The factors of 63 are 1, 3, 7, 9, 21, and 63.

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.

The common factors are 1, 3, 7, and 21.

Therefore, the greatest common factor is 21.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 42 are 2, 3, and 7.

The prime factors of 63 are 3, 3, and 7.

The prime factors of 84 are 2, 2, 3, and 7.

The prime factors in common are 3 and 7, so the greatest common factor is 3 x 7 = 21.

21 is the only positive integer that exhibits the Perfect Progression where if the multiples of 21 up to 210 are placed in to two parallel vertical columns so that the first reads 2, 4, 6, 8, 10 etc and the second 1, 2, 3, 4, 5 etc for example,

2 4

4 2

6 3

8 4

10 5

whereby each in one column multiplied by another number ordered diagonally in the other column equals the multiplication of the opposite diagonal, for example, 2x2 and 1x4 both equal 4, then both opposite diagonal numbers 4x3 and 2x6 equal 12, then both opposite diagonal numbers 6x4 and 3x8 equal 24 and so on.

HCF stands for Highest Common Factor, which is also known as Greatest Common Divisor (GCD). It is the largest positive integer that divides two or more numbers without leaving a remainder. Finding the HCF involves identifying the largest factor that is common to all the numbers being considered.

The common factors of 21 and 133 are the numbers that can evenly divide both 21 and 133 without leaving a remainder. The factors of 21 are 1, 3, 7, and 21, while the factors of 133 are 1, 7, 19, and 133. Therefore, the only common factor of 21 and 133 is 1.

Well, isn't that just a happy little math problem we have here! The greatest common factor of 5, 15, and 30 is 5. You see, the greatest common factor is the largest number that divides evenly into all the numbers you're looking at. Just like painting a beautiful landscape, finding the greatest common factor is all about finding harmony and balance in numbers.

To find the greatest common factor (GCF) of 40, 60, and 90, you need to determine the largest number that divides evenly into all three numbers. First, list the factors of each number: 40 (1, 2, 4, 5, 8, 10, 20, 40), 60 (1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), and 90 (1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90). The GCF of 40, 60, and 90 is 10, as it is the largest number that is a factor of all three numbers.

Well, honey, the number less than 500 with the most factors is 420. It's got a whopping 24 factors, making it the diva of the numbers under 500. So, if you're looking for a number with a lot of friends, 420 is your go-to.

In mathematics, the expression "5 3 and 8" is typically interpreted as a mixed number, which consists of a whole number and a fraction. To convert this mixed number into an improper fraction, you multiply the whole number by the denominator of the fraction and add the numerator. Therefore, "5 3 and 8" can be written as the improper fraction 43/8.

Well, isn't that a happy little question! To find the LCM, we look for the smallest number that all three numbers can divide into evenly. First, we prime factorize each number: 32 = 2^5, 96 = 2^5 * 3, and 160 = 2^5 * 5. Then, we take the highest power of each prime factor present in the prime factorization of each number, which gives us 2^5 * 3 * 5 = 960. So, the LCM of 32, 96, and 160 is 960. Happy calculating!

The common factors of 320 are the numbers that can divide 320 without leaving a remainder. The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, and 320. These numbers can be multiplied together in different combinations to give the original number 320.

8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 256, 264, 272, 280, 288, 296, 304, 312, 320, 328, 336, 344, 352, 360, 368, 376, 384, 392, 400, 408, 416, 424, 432, 440, 448, 456, 464, 472, 480, 488, 496, 504, 512, 520, 528, 536, 544, 552, 560, 568, 576, 584, 592, 600, 608, 616, 624, 632, 640, 648, 656, 664, 672, 680, 688, 696, 704, 712, 720, 728, 736, 744, 752, 760, 768, 776, 784, 792, 800, 808, 816, 824, 832, 840, 848, 856, 864, 872, 880, 888, 896, 904, 912, 920, 928, 936, 944, 952, 960, 968, 976, 984, 992, 1000, 1008, 1016, 1024, 1032, 1040, 1048, 1056, 1064, 1072, 1080, 1088, 1096, 1104, 1112, 1120, 1128, 1136, 1144, 1152, 1160, 1168, 1176, 1184, 1192, 1200, 1208, 1216, 1224, 1232, 1240, 1248, 1256, 1264, 1272, 1280, 1288, 1296, 1304, 1312, 1320, 1328, 1336, 1344, 1352, 1360, 1368, 1376,

1384, 1392, 1400, 1408, 1416, 1424, 1432, 1440, 1448, 1456, 1464, 1472, 1480, 1488, 1496, 1504, 1512, 1520, 1528, 1536, 1544, 1552, 1560, 1568, 1576, 1584, 1592, 1600, 1608, 1616, 1624, 1632, 1640, 1648, 1656, 1664, 1672, 1680, 1688, 1696, 1704, 1712, 1720, 1728, 1736, 1744, 1752, 1760, 1768, 1776, 1784, 1792, 1800, 1808, 1816, 1824, 1832, 1840, 1848, 1856, 1864, 1872, 1880, 1888, 1896, 1904, 1912, 1920, 1928, 1936, 1944, 1952, 1960, 1968, 1976, 1984, 1992, 2000, 2008, 2016, 2024, 2032, 2040, 2048, 2056, 2064, 2072, 2080...

Alright, buckle up buttercup. The Highest Common Factor (HCF) of 280 and 180 is 20. That's right, 20 is the largest number that divides both 280 and 180 without leaving a remainder. So, there you have it, 20 is the HCF you're looking for.

Oh, what a happy little math question! To find four numbers that multiply to 100, we can think of them as pairs of numbers that multiply to 100. One pair is 2 and 50, and the other pair is 4 and 25. Isn't it wonderful how numbers can come together to create beautiful harmony?

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers evenly. To find the GCF of 6 and 8, we need to determine the common factors of both numbers. The factors of 6 are 1, 2, 3, and 6, while the factors of 8 are 1, 2, 4, and 8. The largest number that is common to both sets of factors is 2, making the GCF of 6 and 8 equal to 2.

The least common multiple (LCM) of 14, 28, and 49 can be found by first determining the prime factors of each number. The prime factorization of 14 is 2 x 7, 28 is 2^2 x 7, and 49 is 7^2. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^2 x 7^2 = 196. Therefore, the least common multiple of 14, 28, and 49 is 196.

Well, darling, the highest common factor (HCF) of 120 and 400 is 40. It's like finding the biggest slice of cake you can cut from both numbers without any leftovers. So, grab that 40 and celebrate - you've found the HCF!

To find the Highest Common Factor (HCF) of 1020 and 11594 using the division method, we first divide the larger number, 11594, by the smaller number, 1020.

11594 divided by 1020 gives a quotient of 11 with a remainder of 554.

Next, we divide the divisor, 1020, by the remainder, 554.

1020 divided by 554 gives a quotient of 1 with a remainder of 466.

Continuing this process, we divide 554 by 466, which gives a quotient of 1 with a remainder of 88.

Finally, we divide 466 by 88, which gives a quotient of 5 with a remainder of 46.

Since the remainder is not zero, we continue the process.

Dividing 88 by 46 gives a quotient of 1 with a remainder of 42.

Continuing, we divide 46 by 42, which gives a quotient of 1 with a remainder of 4.

Finally, dividing 42 by 4 gives a quotient of 10 with a remainder of 2.

Since the remainder is not zero, we continue.

Dividing 4 by 2 gives a quotient of 2 with a remainder of 0.

Therefore, the HCF of 1020 and 11594 is 2.

180 = 2 x 2 x 3 x 3 x 5

or

22 x 32 x 5

The multiples of 245 are numbers that can be divided evenly by 245. To find the multiples, you can multiply 245 by whole numbers. The first few multiples of 245 are 245, 490, 735, 980, 1225, and so on.

Oh, dude, you want me to find factor pairs of 10,000? Like, okay, so let's see, there's 1 and 10,000, and 2 and 5,000, and 4 and 2,500, and so on. I mean, there are like a bunch of them, but who's really counting, right? It's like, just a bunch of numbers hanging out together, having a party in the world of math.

To find the Least Common Multiple (LCM) of 136, 102, and 204, we first need to find the prime factorization of each number. The prime factorization of 136 is 2^3 * 17, the prime factorization of 102 is 2 * 3 * 17, and the prime factorization of 204 is 2^2 * 3 * 17. To find the LCM, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3 * 17 = 408. Therefore, the LCM of 136, 102, and 204 is 408.

Oh, dude, like, the factors between 40 and 50 are just the numbers that can be multiplied together to give you a product within that range. So, you've got 41 and 43 as prime numbers, and then you've got 44 which is 4 times 11, and 45 which is 3 times 15, and 46 which is 2 times 23, and 48 which is 4 times 12, and 49 which is 7 times 7. That's it, like, nothing too exciting, just some good old math vibes.