Factoring and Multiples

To factor the polynomial 2x^2 + 16, we first look for a common factor. In this case, both terms are divisible by 2, so we can factor out a 2 to get 2(x^2 + 8). Next, we check if the remaining quadratic expression x^2 + 8 can be factored further. Since x^2 + 8 cannot be factored further over the real numbers, the factored form of the polynomial is 2(x^2 + 8).

x^(2) - x - 56

is a Quadratic EXPRESSION.

This can be factored to

( x + 7)(x - 8)

To find the values of 'x' , it needs to be equated to 'zero'

Hence it is Quadratic EQUATION

x^(2) - x - 56 = 0

( x + 7)(x - 8) = 0

x + 7 = 0

x = -7

& / or

x - 8 = 0

x = 8

To find two numbers that multiply to 416, we need to factorize 416. The prime factorization of 416 is 2^5 * 13. To get the pairs of numbers that multiply to 416, we can combine these factors in different ways. So, the pairs that multiply to 416 are (2, 208), (4, 104), (8, 52), and (16, 26).

Oh, dude, the greatest common factor of 8x and 36 is 4. You just gotta find the highest number that divides evenly into both of them. It's like finding the perfect match on a dating app, but for numbers. So yeah, 4 is the lucky winner here.

Oh, isn't that just lovely? Let's paint a picture with multiples of 7 up to 700. So, we start with 7, then add 7 each time: 7, 14, 21, 28, and so on, all the way up to 700. Just imagine each multiple of 7 as a happy little tree in our mathematical landscape.

Oh, dude, the Greatest Common Factor (GCF) of 16, 48, and 72 is 8. It's like the biggest number that can divide all of them without leaving any remainder. So, if you're throwing a party with 16, 48, and 72 guests, you can totally divide them into groups of 8 for some epic party games.

To find the highest common factor (HCF) of 48 and 224, we need to identify the common factors of both numbers. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48. The factors of 224 are 1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, and 224. The highest common factor of 48 and 224 is 16, as it is the greatest number that divides both 48 and 224 without leaving a remainder.

Oh, what a happy little question! Let's take a moment to appreciate these numbers. Between 61 and 107, the multiples of 4 are 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, and 104. The multiples of 8 are 64, 72, 80, 88, 96, and the multiples of 16 are 64 and 80. Just like painting a beautiful landscape, finding these multiples can be a calming and rewarding experience.

Oh, what a lovely question! Let's see here... Ah, I see a beautiful number peeking through the canvas. The number 72 fits perfectly between 55 and 101, and it is a multiple of 3, 6, and 8. Just like adding happy little trees to a painting, numbers can come together in harmony.

25

The common multiples of 2 and 6 are numbers that can be divided evenly by both 2 and 6. To find these common multiples, we first list the multiples of each number. The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, etc., and the multiples of 6 are 6, 12, 18, 24, 30, 36, etc. The common multiples of 2 and 6 are the numbers that appear in both lists, such as 6, 12, 18, etc.

The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498, 504, 510, 516, 522, 528, 534, 540, 546, 552, 558, 564, 570, 576, 582, 588, 594, 600, 606, 612, 618, 624, 630, 636, 642, 648, 654, 660, 666, 672, 678, 684, 690, 696, 702, 708, 714, 720, 726, 732, 738, 744, 750, 756, 762, 768, 774, 780, 786, 792, 798, 804, 810, 816, 822, 828, 834, 840, 846, 852, 858, 864, 870, 876, 882, 888, 894, 900, 906, 912, 918, 924, 930, 936, 942, 948, 954, 960, 966, 972, 978, 984, 990, 996, 1002, 1008, 1014, 1020, 1026, 1032, 1038, 1044, 1050, 1056, 1062, 1068, 1074, 1080, 1086, 1092, 1098, 1104, 1110, 1116, 1122, 1128, 1134, 1140, 1146, 1152, 1158, 1164, 1170, 1176, 1182, 1188, 1194, 1200, 1206, 1212, 1218, 1224, 1230, 1236, 1242, 1248, 1254, 1260, 1266, 1272, 1278, 1284, 1290, 1296, 1302, 1308, 1314, 1320, 1326, 1332, 1338, 1344, 1350, 1356, 1362, 1368, 1374, 1380, 1386, 1392, 1398, 1404, 1410, 1416, 1422, 1428, 1434, 1440, 1446, 1452, 1458, 1464, 1470, 1476, 1482, 1488, 1494, 1500, 1506, 1512, 1518, 1524, 1530, 1536, 1542, 1548, 1554, 1560, 1566, 1572, 1578, 1584, 1590, 1596, 1602, 1608, 1614, 1620, 1626, 1632, 1638, 1644, 1650, 1656, 1662, 1668, 1674, 1680, 1686, 1692, 1698, 1704, 1710, 1716, 1722, 1728, 1734, 1740, 1746, 1752, 1758, 1764, 1770, 1776, 1782, 1788, 1794, 1800, 1806, 1812, 1818, 1824, 1830, 1836, 1842, 1848, 1854, 1860, 1866, 1872, 1878, 1884, 1890, 1896, 1902, 1908, 1914, 1920, 1926, 1932, 1938, 1944, 1950, 1956, 1962, 1968, 1974, 1980, 1986, 1992, 1998, 2004, 2010, 2016, 2022, 2028, 2034, 2040, 2046, 2052, 2058, 2064, 2070, 2076, 2082, 2088, 2094, 2100, 2106, 2112, 2118, 2124, 2130, 2136, 2142, 2148, 2154, 2160, 2166, 2172, 2178, 2184, 2190, 2196, 2202, 2208, 2214, 2220, 2226, 2232, 2238, 2244, 2250, 2256, 2262, 2268, 2274, 2280, 2286, 2292, 2298, 2304, 2310, 2316, 2322, 2328, 2334, 2340, 2346, 2352, 2358, 2364, 2370, 2376, 2382, 2388, 2394, 2400, 2406, 2412, 2418, 2424, 2430, 2436, 2442, 2448, 2454, 2460, 2466, 2472, 2478, 2484, 2490, 2496, 2502, 2508, 2514, 2520, 2526, 2532, 2538, 2544, 2550, 2556, 2562, 2568, 2574, 2580, 2586, 2592, 2598, 2604, 2610, 2616, 2622, 2628, 2634, 2640, 2646, 2652, 2658, 2664, 2670, 2676, 2682, 2688, 2694, 2700, 2706, 2712, 2718, 2724, 2730, 2736, 2742, 2748, 2754, 2760, 2766, 2772, 2778, 2784, 2790, 2796, 2802, 2808, 2814, 2820, 2826, 2832, 2838, 2844, 2850, 2856, 2862, 2868, 2874, 2880, 2886, 2892, 2898, 2904, 2910, 2916, 2922, 2928, 2934, 2940, 2946, 2952, 2958, 2964, 2970, 2976, 2982, 2988, 2994, 3000, 3006, 3012, 3018, 3024, 3030, 3036, 3042, 3048, 3054, 3060, 3066, 3072, 3078, 3084, 3090, 3096, 3102, 3108, 3114, 3120, 3126, 3132, 3138, 3144, 3150, 3156, 3162, 3168, 3174, 3180, 3186, 3192, 3198, 3204, 3210, 3216, 3222, 3228, 3234, 3240, 3246, 3252, 3258, 3264, 3270, 3276, 3282, 3288, 3294, 3300, 3306, 3312, 3318, 3324, 3330, 3336, 3342, 3348, 3354, 3360, 3366, 3372, 3378, 3384, 3390, 3396, 3402, 3408, 3414, 3420, 3426, 3432, 3438, 3444, 3450, 3456, 3462, 3468, 3474, 3480, 3486, 3492, 3498, 3504, 3510, 3516, 3522, 3528, 3534, 3540, 3546, 3552, 3558, 3564, 3570, 3576, 3582, 3588, 3594, 3600, 3606, 3612, 3618, 3624, 3630, 3636, 3642, 3648, 3654, 3660, 3666, 3672, 3678, 3684, 3690, 3696, 3702, 3708, 3714, 3720, 3726, 3732, 3738, 3744, 3750, 3756, 3762, 3768, 3774, 3780, 3786, 3792, 3798, 3804, 3810, 3816, 3822, 3828, 3834, 3840, 3846, 3852, 3858, 3864, 3870, 3876, 3882, 3888, 3894, 3900, 3906, 3912, 3918, 3924, 3930, 3936, 3942, 3948, 3954, 3960, 3966, 3972, 3978, 3984, 3990, 3996, 4002, 4008, 4014, 4020, 4026, 4032, 4038, 4044, 4050, 4056, 4062, 4068, 4074, 4080, 4086, 4092, 4098, 4104, 4110, 4116, 4122, 4128, 4134, 4140, 4146, 4152, 4158, 4164, 4170, 4176, 4182, 4188, 4194, 4200, 4206, 4212, 4218, 4224, 4230, 4236, 4242, 4248, 4254, 4260, 4266, 4272, 4278, 4284, 4290, 4296, 4302, 4308, 4314, 4320, 4326, 4332, 4338, 4344, 4350, 4356, 4362, 4368, 4374, 4380, 4386, 4392, 4398, 4404, 4410, 4416, 4422, 4428, 4434, 4440, 4446, 4452, 4458, 4464, 4470, 4476, 4482, 4488, 4494, 4500, 4506, 4512, 4518, 4524, 4530, 4536, 4542, 4548, 4554, 4560, 4566, 4572, 4578, 4584, 4590, 4596, 4602, 4608, 4614, 4620, 4626, 4632, 4638, 4644, 4650, 4656, 4662, 4668, 4674, 4680, 4686, 4692, 4698, 4704, 4710, 4716, 4722, 4728, 4734, 4740, 4746, 4752, 4758, 4764, 4770, 4776, 4782, 4788, 4794, 4800, 4806, 4812, 4818, 4824, 4830, 4836, 4842, 4848, 4854, 4860, 4866, 4872, 4878,

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by nathman4 #my username on roblox

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The positive integer multiples of 12 with products lower than 400 are:

12 x 1 = 12

12 x 2 = 24

12 x 3 = 36

12 x 4 = 48

12 x 5 = 60

12 x 6 = 72

12 x 7 = 84

12 x 8 = 96

12 x 9 = 108

12 x 10 = 120

12 x 11 = 132

12 x 12 = 144

12 x 13 = 156

12 x 14 = 168

12 x 15 = 180

12 x 16 = 192

12 x 17 = 204

12 x 18 = 216

12 x 19 = 228

12 x 20 = 240

12 x 21 = 252

12 x 22 = 264

12 x 23 = 276

12 x 24 = 288

12 x 25 = 300

12 x 26 = 312

12 x 27 = 324

12 x 28 = 336

12 x 29 = 348

12 x 30 = 360

12 x 31 = 372

12 x 32 = 384

12 x 33 = 396

The greatest common factor (GCF) of 27, 36, and 81 is 9. To find the GCF, we need to determine the largest number that divides evenly into all three numbers. In this case, 9 is the largest number that is a factor of 27, 36, and 81, making it the greatest common factor.

Well, honey, the least common multiple of 5, 9, and 27 is 135. It's like finding the perfect outfit that fits all three of them without any alterations needed. So, grab that LCM like it's the last piece of cheesecake at a Golden Girls marathon!

The number in question can be found by multiplying the prime factors together: 2 x 7 x 11 = 154. This means that 154 is the smallest number with these prime factors. In general, the prime factorization of a number involves breaking it down into its prime factors, which are the smallest prime numbers that divide evenly into the original number.

Well, honey, the least common multiple (LCM) of 210 and 280 is 840. It's like finding the perfect pair of shoes that both 210 and 280 can comfortably walk in together without any toe-stepping. So, there you have it, 840 is the magic number that makes both 210 and 280 happy campers.

There are no factors of 50 in that range.

Well, honey, the greatest common factor of 15, 25, and 50 is 5. It's like finding the perfect little black dress that fits all three numbers like a glove. So, go ahead and strut your stuff knowing you've found that common factor.

The multiples of 268 are the products of 268 and any non-zero integer. Some of the multiples of 268 include 536, 804, 1072, and so on. These numbers can be obtained by multiplying 268 by 1, 2, 3, 4, and so forth.

The common factors of 264 and 504 are the numbers that can evenly divide both 264 and 504 without leaving a remainder. To find the common factors, we first need to find the prime factorization of each number. The prime factorization of 264 is 2^3 * 3 * 11, and the prime factorization of 504 is 2^3 * 3^2 * 7. The common factors are the common prime factors raised to the lowest power they appear in both numbers, which in this case are 2^3 and 3. Therefore, the common factors of 264 and 504 are 2^3 (8) and 3.

Well, honey, the factors of 16 are 1, 2, 4, 8, and 16. Now, if you line them up in numerical order, the middle number is 4. So, the median of the factors of 16 is 4. Hope that clears things up for ya, sugar!

Well, aren't you just a math whiz! The greatest common factor of 28 and 34 is actually 2. Looks like you've got a knack for numbers, keep up the good work!

The Highest Common Factor (HCF) of two numbers is the largest number that divides both numbers without leaving a remainder. To find the HCF of 126 and 147, we need to find the common factors of both numbers. The factors of 126 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, and 126. The factors of 147 are 1, 3, 7, 21, 49, and 147. The highest common factor of 126 and 147 is 21.