Factoring and Multiples

I not a human calcuator so don't ask me.

Also me: HuMaN calculator.

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

60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.

The greatest common factor for 60 and 210 is 30.

Oh, dude, you're really making me do math right now? Fine, fine. So, 92 can be expressed as 2 x 2 x 23. There you go, a thrilling adventure into the world of prime factors. Hope you enjoyed the ride!

The Highest Common Factor (HCF) of 21, 77, and 84 is 7. To find the HCF, you need to identify the common factors of the numbers and determine the highest one they all share. In this case, the factors of 21 are 1, 3, 7, 21; the factors of 77 are 1, 7, 11, 77; and the factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The highest common factor among them is 7.

Oh, dude, you're hitting me with the math questions now? Alright, so the prime factors of 24 in index form would be 2^3 * 3^1. Basically, you break down 24 into its prime numbers and count how many times each prime number appears. So, 2 is raised to the power of 3 because it appears 3 times in 24, and 3 is raised to the power of 1 because it appears once. Math class is in session!

Well, honey, 5 can't go into 0 unless you want to break the laws of mathematics. You see, division by zero is a big no-no in the math world because it leads to all sorts of chaos and confusion. So, in short, 5 cannot go into 0 unless you're playing make-believe.

Well, darling, it's simple math. 1 times 135 equals 135. But if you want to get fancy, you could also say 3 times 45 equals 135. So, take your pick and go forth with your newfound multiplication knowledge.

Oh, dude, let me break it down for you. So, 912 is a multiple of 6 because when you divide 912 by 6, you get a whole number without any remainders. It's like when you have a pizza and you can divide it into 6 equal slices, with no pesky crust left over. So yeah, 912 is totally chill with being a multiple of 6.

6 can be divided by 1, 2, 3, and 6. This is because division is the process of splitting a number into equal parts. In the case of 6, it can be evenly divided by these numbers without leaving a remainder.

1 x 215, 5 x 43

Zero has an infinite number of factors.

Explanation

Oh, dude, it's like you take 7035 and break it down into its parts. So, 7035 is like 7 x 1000 + 0 x 100 + 3 x 10 + 5 x 1. Then you can write it in exponent form as 7 x 10^3 + 0 x 10^2 + 3 x 10^1 + 5 x 10^0. Boom, there you go!

To determine how many times 15 goes into 75, you would divide 75 by 15. The result of this division is 5, which means that 15 goes into 75 exactly 5 times. This can be expressed as 75 ÷ 15 = 5.

The factor pairs of 75 are:

1 × 75

3 × 25

5 × 15

Well, darling, the Least Common Multiple (LCM) of 4, 9, and 2 is 36. It's the smallest multiple that all three numbers can divide into without leaving a pesky remainder. So, there you have it, 36 is the magic number that keeps these three amigos happy.

Well, darling, the highest common factor of 78, 91, and 156 is 13. It's like finding the perfect pair of shoes that goes with every outfit - simple and essential. So, there you have it, 13 is the magic number that can divide all three of those numbers without a fuss.

Assuming you mean the numbers between 1 and 1000 which are multiple of 8, they are:

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

If you mean the first 1000 multiples of 8, they are the above plus:

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, 2088, 2096, 2104, 2112, 2120, 2128, 2136, 2144, 2152, 2160, 2168, 2176, 2184, 2192, 2200, 2208, 2216, 2224, 2232, 2240, 2248, 2256, 2264, 2272, 2280, 2288, 2296, 2304, 2312, 2320, 2328, 2336, 2344, 2352, 2360, 2368, 2376, 2384, 2392, 2400, 2408, 2416, 2424, 2432, 2440, 2448, 2456, 2464, 2472, 2480, 2488, 2496, 2504, 2512, 2520, 2528, 2536, 2544, 2552, 2560, 2568, 2576, 2584, 2592, 2600, 2608, 2616, 2624, 2632, 2640, 2648, 2656, 2664, 2672, 2680, 2688, 2696, 2704, 2712, 2720, 2728, 2736, 2744, 2752, 2760, 2768, 2776, 2784, 2792, 2800, 2808, 2816, 2824, 2832, 2840, 2848, 2856, 2864, 2872, 2880, 2888, 2896, 2904, 2912, 2920, 2928, 2936, 2944, 2952, 2960, 2968, 2976, 2984, 2992, 3000, 3008, 3016, 3024, 3032, 3040, 3048, 3056, 3064, 3072, 3080, 3088, 3096, 3104, 3112, 3120, 3128, 3136, 3144, 3152, 3160, 3168, 3176, 3184, 3192, 3200, 3208, 3216, 3224, 3232, 3240, 3248, 3256, 3264, 3272, 3280, 3288, 3296, 3304, 3312, 3320, 3328, 3336, 3344, 3352, 3360, 3368, 3376, 3384, 3392, 3400, 3408, 3416, 3424, 3432, 3440, 3448, 3456, 3464, 3472, 3480, 3488, 3496, 3504, 3512, 3520, 3528, 3536, 3544, 3552, 3560, 3568, 3576, 3584, 3592, 3600, 3608, 3616, 3624, 3632, 3640, 3648, 3656, 3664, 3672, 3680, 3688, 3696, 3704, 3712, 3720, 3728, 3736, 3744, 3752, 3760, 3768, 3776, 3784, 3792, 3800, 3808, 3816, 3824, 3832, 3840, 3848, 3856, 3864, 3872, 3880, 3888, 3896, 3904, 3912, 3920, 3928, 3936, 3944, 3952, 3960, 3968, 3976, 3984, 3992, 4000, 4008, 4016, 4024, 4032, 4040, 4048, 4056, 4064, 4072, 4080, 4088, 4096, 4104, 4112, 4120, 4128, 4136, 4144, 4152, 4160, 4168, 4176, 4184, 4192, 4200, 4208, 4216, 4224, 4232, 4240, 4248, 4256, 4264, 4272, 4280, 4288, 4296, 4304, 4312, 4320, 4328, 4336, 4344, 4352, 4360, 4368, 4376, 4384, 4392, 4400, 4408, 4416, 4424, 4432, 4440, 4448, 4456, 4464, 4472, 4480, 4488, 4496, 4504, 4512, 4520, 4528, 4536, 4544, 4552, 4560, 4568, 4576, 4584, 4592, 4600, 4608, 4616, 4624, 4632, 4640, 4648, 4656, 4664, 4672, 4680, 4688, 4696, 4704, 4712, 4720, 4728, 4736, 4744, 4752, 4760, 4768, 4776, 4784, 4792, 4800, 4808, 4816, 4824, 4832, 4840, 4848, 4856, 4864, 4872, 4880, 4888, 4896, 4904, 4912, 4920, 4928, 4936, 4944, 4952, 4960, 4968, 4976, 4984, 4992, 5000, 5008, 5016, 5024, 5032, 5040, 5048, 5056, 5064, 5072, 5080, 5088, 5096, 5104, 5112, 5120, 5128, 5136, 5144, 5152, 5160, 5168, 5176, 5184, 5192, 5200, 5208, 5216, 5224, 5232, 5240, 5248, 5256, 5264, 5272, 5280, 5288, 5296, 5304, 5312, 5320, 5328, 5336, 5344, 5352, 5360, 5368, 5376, 5384, 5392, 5400, 5408, 5416, 5424, 5432, 5440, 5448, 5456, 5464, 5472, 5480, 5488, 5496, 5504, 5512, 5520, 5528, 5536, 5544, 5552, 5560, 5568, 5576, 5584, 5592, 5600, 5608, 5616, 5624, 5632, 5640, 5648, 5656, 5664, 5672, 5680, 5688, 5696, 5704, 5712, 5720, 5728, 5736, 5744, 5752, 5760, 5768, 5776, 5784, 5792, 5800, 5808, 5816, 5824, 5832, 5840, 5848, 5856, 5864, 5872, 5880, 5888, 5896, 5904, 5912, 5920, 5928, 5936, 5944, 5952, 5960, 5968, 5976, 5984, 5992, 6000, 6008, 6016, 6024, 6032, 6040, 6048, 6056, 6064, 6072, 6080, 6088, 6096, 6104, 6112, 6120, 6128, 6136, 6144, 6152, 6160, 6168, 6176, 6184, 6192, 6200, 6208, 6216, 6224, 6232, 6240, 6248, 6256, 6264, 6272, 6280, 6288, 6296, 6304, 6312, 6320, 6328, 6336, 6344, 6352, 6360, 6368, 6376, 6384, 6392, 6400, 6408, 6416, 6424, 6432, 6440, 6448, 6456, 6464, 6472, 6480, 6488, 6496, 6504, 6512, 6520, 6528, 6536, 6544, 6552, 6560, 6568, 6576, 6584, 6592, 6600, 6608, 6616, 6624, 6632, 6640, 6648, 6656, 6664, 6672, 6680, 6688, 6696, 6704, 6712, 6720, 6728, 6736, 6744, 6752, 6760, 6768, 6776, 6784, 6792, 6800, 6808, 6816, 6824, 6832, 6840, 6848, 6856, 6864, 6872, 6880, 6888, 6896, 6904, 6912, 6920, 6928, 6936, 6944, 6952, 6960, 6968, 6976, 6984, 6992, 7000, 7008, 7016, 7024, 7032, 7040, 7048, 7056, 7064, 7072, 7080, 7088, 7096, 7104, 7112, 7120, 7128, 7136, 7144, 7152, 7160, 7168, 7176, 7184, 7192, 7200, 7208, 7216, 7224, 7232, 7240, 7248, 7256, 7264, 7272, 7280, 7288, 7296, 7304, 7312, 7320, 7328, 7336, 7344, 7352, 7360, 7368, 7376, 7384, 7392, 7400, 7408, 7416, 7424, 7432, 7440, 7448, 7456, 7464, 7472, 7480, 7488, 7496, 7504, 7512, 7520, 7528, 7536, 7544, 7552, 7560, 7568, 7576, 7584, 7592, 7600, 7608, 7616, 7624, 7632, 7640, 7648, 7656, 7664, 7672, 7680, 7688, 7696, 7704, 7712, 7720, 7728, 7736, 7744, 7752, 7760, 7768, 7776, 7784, 7792, 7800, 7808, 7816, 7824, 7832, 7840, 7848, 7856, 7864, 7872, 7880, 7888, 7896, 7904, 7912, 7920, 7928, 7936, 7944, 7952, 7960, 7968, 7976, 7984, 7992, 8000

Hope this helped :D

The greatest common factor (GCF) refers to a factor that is COMMON to two or more numbers. You have only one number in the question! The greatest factor of any number is itself.

There is neither a greatest common factor nor common factors of a single number, such as 42, because there cannot be any form of common factor without two or more numbers to compare. Common factors are factors that the numbers being compared have in common. The greatest common factor is the largest factor that all the numbers being compared have in common. Thus, since there are not two or more numbers to compare, there are neither common factors nor a greatest common factor.

The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Examples: The common factors of 25 and 42 are only 1; the greatest common factor is 1.

The common factors of 36 and 42 are 1, 2, 3, and 6; the greatest common factor is 6.

The common factors of 42 and 49 are 1 and 7; the greatest common factor is 7.

The common factors of 42 and 60 are 1, 2, 3, and 6; the greatest common factor is 6.

The common factors of 42 and 70 are 1, 2, 7, and 14; the greatest common factor is 14.

To find the Least Common Multiple (LCM) of 5, 25, and 125, we need to first find the prime factorization of each number. The prime factorization of 5 is 5, the prime factorization of 25 is 5^2, and the prime factorization of 125 is 5^3. The LCM is the product of the highest power of each prime factor that appears in any of the numbers, which in this case is 5^3, equaling 125. Therefore, the LCM of 5, 25, and 125 is 125.

Ah, let's take a moment to appreciate the beauty of numbers. The common factors of 135 and 210 are the numbers that can divide both of them evenly. In this case, the common factors of 135 and 210 are 1, 3, 5, and 15. Just like in painting, finding common factors is about discovering harmony and balance in numbers.

The least common multiple (LCM) is often also called the lowest common multiple or smallest common multiple. Keep in mind that these different terms all refer to the same thing: the smallest positive integer which is a multiple of two or more numbers.

The least common multiple of 5, 25, and 125 is 125.

63 and 21

42 and 42

three twenty-eights

four twenty-ones

six fourteens

seven twelves

twelve sevens

fourteen sixes

twenty-one fours

twenty-eight threes

forty-two twos

eighty-four ones

Well, isn't that a happy little question! If you take the numbers 400, 500, and 30, and add them together with a gentle brush stroke, you'll find they equal 930. Just like painting a beautiful landscape, sometimes all you need is the right combination of colors and numbers to create something truly wonderful.

Oh, dude, the least common multiple of 32 and 128 is 128. Like, you take the bigger number because it's already a multiple of the smaller one. So, yeah, 128 is the least common multiple. Easy peasy lemon squeezy.