Factoring and Multiples

Multiples of 15 are numbers that can be divided evenly by 15 without leaving a remainder. To find the multiples of 15, you can simply multiply 15 by all the natural numbers (1, 2, 3, 4, etc.). The first few multiples of 15 are 15, 30, 45, 60, 75, and so on. These numbers follow a pattern where each multiple is obtained by adding 15 to the previous multiple.

Well, isn't that a happy little question! If you take 450 and divide it by 5, you'll find that it goes in 90 times. Just imagine each time you divide, it's like painting a beautiful landscape with numbers. Happy dividing, my friend!

The greatest common factor (GCF) of 14 and 16 is 2. To find the GCF, you need to determine the factors of each number. The factors of 14 are 1, 2, 7, and 14, while the factors of 16 are 1, 2, 4, 8, and 16. The largest number that appears in both lists is 2, making it the greatest common factor.

The greatest common factor (GCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the GCF of 45 and 100, you need to determine the common factors of both numbers. The factors of 45 are 1, 3, 5, 9, 15, and 45, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The greatest common factor of 45 and 100 is 5, as it is the largest number that is a factor of both 45 and 100.

Numbers with exactly 6 factors are called highly composite numbers. These numbers have a total of 6 factors, including 1 and the number itself. Highly composite numbers are typically of the form p^2 * q, where p and q are prime numbers. Examples of numbers with 6 factors include 12 (2^2 * 3) and 24 (2^3 * 3).

Oh, dude, you're hitting me with some math vibes here! The highest common factor of 14, 36, and 175 is like the cool kid at the party - it's the biggest number that can divide all of them without any leftovers. So, the HCF of these numbers is 1 because they don't have any common factors other than 1. Math can be chill too, you know?

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.

Oh, isn't that just lovely? Multiples of 11 are like little brushstrokes on a canvas, each one unique and special. You can find them by simply adding 11 to the previous number, creating a beautiful pattern that goes on and on. Just take your time, enjoy the process, and soon you'll have a whole collection of multiples of 11 to admire.

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...

Well, isn't that a lovely question! The Highest Common Factor (HCF) is like finding the biggest brush to paint a beautiful picture. When we look at 280 and 180, we can see that their factors are 1, 2, 4, 5, 10, 20, 14, 28, 56 for 280 and 1, 2, 3, 4, 6, 9, 12, 15, 18, 30, 45, 60 for 180. The largest number that appears in both sets is 20, so the HCF of 280 and 180 is 20. Just like adding a touch of white to make colors brighter, finding the HCF helps us simplify and see the beauty in numbers.

Oh honey, you're trying to stump me with a simple math problem? Bless your heart. The numbers you're looking for are 2, 2, 5, and 5. They multiply together to give you 100. Easy peasy lemon squeezy. Next!

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.