Factoring and Multiples

Oh, what a lovely question! Finding the Highest Common Factor (HCF) is like finding the common thread that ties these numbers together. If we look at 36, 42, and 54, we can see that the largest number that divides them all evenly is 6. So, the HCF for 36, 42, and 54 is 6. Just like how different colors blend together to create a beautiful painting, these numbers come together harmoniously with 6 as their HCF.

The greatest common factor of 15 18 and 24 is 3.

The GCF is 3.

The factor monomial for 30x^2y is the simplest expression that can be factored out from the given monomial. In this case, the factor monomial is 10xy, which is obtained by finding the greatest common factor of the coefficients and variables in the expression. This factor monomial represents the common terms shared by all parts of the original monomial, making it easier to work with in algebraic expressions.

45 as 15x3 or 9x5
also then 90 135 180 225 270 315 360
and so on

.01, .02, .04, .06, .12, .24

To determine if 42 is divisible by 3, you can add up the digits of 42 (4 + 2 = 6) and check if the sum is divisible by 3. Since 6 is divisible by 3, then 42 is also divisible by 3. This is based on the rule that a number is divisible by 3 if the sum of its digits is divisible by 3.

Oh, what a happy little math problem we have here! Let's think about this together. The numbers that multiply to 20 and add up to -10 are -2 and -8. When you multiply them, you get 20, and when you add them, you get -10. Isn't that just a lovely solution? Happy math-ing, my friend!

HCF(60, 108) = 12

Ieast common multiple of 4,10,3

Well, isn't that a happy little question! To find the Least Common Multiple (LCM) of 288 and 39, we can first find the prime factorization of each number. Then, we can multiply the highest power of each prime factor to get the LCM. It's like mixing different colors on your palette to create a beautiful new shade!

To find two numbers that multiply to 1890, we can start by finding the prime factorization of 1890. 1890 can be expressed as 2 x 3 x 3 x 3 x 5 x 7. From this, we can see that 30 x 63 equals 1890. Therefore, the two numbers that multiply to 1890 are 30 and 63.

Oh, dude, the least common multiple of 2, 6, and 7 is 42. It's like the number that all three of these numbers can divide into evenly without any remainder. So yeah, 42 is the magic number that keeps them all happy.

The LCM (Least Common Multiple) of 25 and 30 is the smallest number that is a multiple of both 25 and 30. To find the LCM, we first need to find the prime factorization of each number: 25 = 5^2 and 30 = 2 * 3 * 5. Then, we take the highest power of each prime factor that appears in either number: 2^1 * 3^1 * 5^2 = 150. Therefore, the LCM of 25 and 30 is 150.

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228, 232, 236, 240, 244, 248, 252, 256, 260, 264, 268, 272, 276, 280, 284, 288, 292, 296, 300, 304, 308, 312, 316, 320, 324, 328, 332, 336, 340, 344, 348, 352, 356, 360, 364, 368, 372, 376, 380, 384, 388, 392, 396, 400, 404, 408, 412, 416, 420, 424, 428, 432, 436, 440, 444, 448, 452, 456, 460, 464, 468, 472, 476, 480, 484, 488, 492, 496, 500, 504, 508, 512, 516, 520, 524, 528, 532, 536, 540, 544, 548, 552, 556, 560, 564, 568, 572, 576, 580, 584, 588, 592, 596, 600, 604, 608, 612, 616, 620, 624, 628, 632, 636, 640, 644, 648, 652, 656, 660, 664, 668, 672, 676, 680, 684, 688, 692, 696, 700, 704, 708, 712, 716, 720, 724, 728, 732, 736, 740, 744, 748, 752, 756, 760, 764, 768, 772, 776, 780, 784, 788, 792, 796, 800, 804, 808, 812, 816, 820, 824, 828, 832, 836, 840, 844, 848, 852, 856, 860, 864, 868, 872, 876, 880, 884, 888, 892, 896, 900, 904, 908, 912, 916, 920, 924, 928, 932, 936, 940, 944, 948, 952, 956, 960, 964, 968, 972, 976, 980, 984, 988, 992, 996, 1000, 1004, 1008, 1012, 1016, 1020, 1024, 1028, 1032, 1036, 1040, 1044, 1048, 1052, 1056, 1060, 1064, 1068, 1072, 1076, 1080, 1084, 1088, 1092, 1096, 1100, 1104, 1108, 1112, 1116, 1120, 1124, 1128, 1132, 1136, 1140, 1144, 1148, 1152, 1156, 1160, 1164, 1168, 1172, 1176, 1180, 1184, 1188, 1192, 1196, 1200, 1204, 1208, 1212, 1216, 1220, 1224, 1228, 1232, 1236, 1240, 1244, 1248, 1252, 1256, 1260, 1264, 1268, 1272, 1276, 1280, 1284, 1288, 1292, 1296, 1300, 1304, 1308, 1312, 1316, 1320, 1324, 1328, 1332, 1336, 1340, 1344, 1348, 1352, 1356, 1360, 1364, 1368, 1372, 1376, 1380, 1384, 1388, 1392, 1396, 1400, 1404, 1408, 1412, 1416, 1420, 1424, 1428, 1432, 1436, 1440, 1444, 1448, 1452, 1456, 1460, 1464, 1468, 1472, 1476, 1480, 1484, 1488, 1492, 1496, 1500, 1504, 1508, 1512, 1516, 1520, 1524, 1528, 1532, 1536, 1540, 1544, 1548, 1552, 1556, 1560, 1564, 1568, 1572, 1576, 1580, 1584, 1588, 1592, 1596, 1600, 1604, 1608, 1612, 1616, 1620, 1624, 1628, 1632, 1636, 1640, 1644, 1648, 1652, 1656, 1660, 1664, 1668, 1672, 1676, 1680, 1684, 1688, 1692, 1696, 1700, 1704, 1708, 1712, 1716, 1720, 1724, 1728, 1732, 1736, 1740, 1744, 1748, 1752, 1756, 1760, 1764, 1768, 1772, 1776, 1780, 1784, 1788, 1792, 1796, 1800, 1804, 1808, 1812, 1816, 1820, 1824, 1828, 1832, 1836, 1840, 1844, 1848, 1852, 1856, 1860, 1864, 1868, 1872, 1876, 1880, 1884, 1888, 1892, 1896, 1900, 1904, 1908, 1912, 1916, 1920, 1924, 1928, 1932, 1936, 1940, 1944, 1948, 1952, 1956, 1960, 1964, 1968, 1972, 1976, 1980, 1984, 1988, 1992, 1996, 2000, 2004, 2008, 2012, 2016, 2020, 2024, 2028, 2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076, 2080, 2084, 2088, 2092, 2096, 2100, 2104, 2108, 2112, 2116, 2120, 2124, 2128, 2132, 2136, 2140, 2144, 2148, 2152, 2156, 2160, 2164, 2168, 2172, 2176, 2180, 2184, 2188, 2192, 2196, 2200, 2204, 2208, 2212, 2216, 2220, 2224, 2228, 2232, 2236, 2240, 2244, 2248, 2252, 2256, 2260, 2264, 2268, 2272, 2276, 2280, 2284, 2288, 2292, 2296, 2300, 2304, 2308, 2312, 2316, 2320, 2324, 2328, 2332, 2336, 2340, 2344, 2348, 2352, 2356, 2360, 2364, 2368, 2372, 2376, 2380, 2384, 2388, 2392, 2396, 2400, 2404, 2408, 2412, 2416, 2420, 2424, 2428, 2432, 2436, 2440, 2444, 2448, 2452, 2456, 2460, 2464, 2468, 2472, 2476, 2480, 2484, 2488, 2492, 2496, 2500, 2504, 2508, 2512, 2516, 2520, 2524, 2528, 2532, 2536, 2540, 2544, 2548, 2552, 2556, 2560, 2564, 2568, 2572, 2576, 2580, 2584, 2588, 2592, 2596, 2600, 2604, 2608, 2612, 2616, 2620, 2624, 2628, 2632, 2636, 2640, 2644, 2648, 2652, 2656, 2660, 2664, 2668, 2672, 2676, 2680, 2684, 2688, 2692, 2696, 2700, 2704, 2708, 2712, 2716, 2720, 2724, 2728, 2732, 2736, 2740, 2744, 2748, 2752, 2756, 2760, 2764, 2768, 2772, 2776, 2780, 2784, 2788, 2792, 2796, 2800, 2804, 2808, 2812, 2816, 2820, 2824, 2828, 2832, 2836, 2840, 2844, 2848, 2852, 2856, 2860, 2864, 2868, 2872, 2876, 2880, 2884, 2888, 2892, 2896, 2900, 2904, 2908, 2912, 2916, 2920, 2924, 2928, 2932, 2936, 2940, 2944, 2948, 2952, 2956, 2960, 2964, 2968, 2972, 2976, 2980, 2984, 2988, 2992, 2996, 3000, 3004, 3008, 3012, 3016, 3020, 3024, 3028, 3032, 3036, 3040, 3044, 3048, 3052, 3056, 3060, 3064, 3068, 3072, 3076, 3080, 3084, 3088, 3092, 3096, 3100, 3104, 3108, 3112, 3116, 3120, 3124, 3128, 3132, 3136, 3140, 3144, 3148, 3152, 3156, 3160, 3164, 3168, 3172, 3176, 3180, 3184, 3188, 3192, 3196, 3200, 3204, 3208, 3212, 3216, 3220, 3224, 3228, 3232, 3236, 3240, 3244, 3248, 3252, 3256, 3260, 3264, 3268, 3272, 3276, 3280, 3284, 3288, 3292, 3296, 3300, 3304, 3308, 3312, 3316, 3320, 3324, 3328, 3332, 3336, 3340, 3344, 3348, 3352, 3356, 3360, 3364, 3368, 3372, 3376, 3380, 3384, 3388, 3392, 3396, 3400, 3404, 3408, 3412, 3416, 3420, 3424, 3428, 3432, 3436, 3440, 3444, 3448, 3452, 3456, 3460, 3464, 3468, 3472, 3476, 3480, 3484, 3488, 3492, 3496, 3500, 3504, 3508, 3512, 3516, 3520, 3524, 3528, 3532, 3536, 3540, 3544, 3548, 3552, 3556, 3560, 3564, 3568, 3572, 3576, 3580, 3584, 3588, 3592, 3596, 3600, 3604, 3608, 3612, 3616, 3620, 3624, 3628, 3632, 3636, 3640, 3644, 3648, 3652, 3656, 3660, 3664, 3668, 3672, 3676, 3680, 3684, 3688, 3692, 3696, 3700, 3704, 3708, 3712, 3716, 3720, 3724, 3728, 3732, 3736, 3740, 3744, 3748, 3752, 3756, 3760, 3764, 3768, 3772, 3776, 3780, 3784, 3788, 3792, 3796, 3800, 3804, 3808, 3812, 3816, 3820, 3824, 3828, 3832, 3836, 3840, 3844, 3848, 3852, 3856, 3860, 3864, 3868, 3872, 3876, 3880, 3884, 3888, 3892, 3896, 3900, 3904, 3908, 3912, 3916, 3920, 3924, 3928, 3932, 3936, 3940, 3944, 3948, 3952, 3956, 3960, 3964, 3968, 3972, 3976, 3980, 3984, 3988, 3992, 3996, 4000.

Since 3y2 can evenly divide 24y3, 3y2 must be the greatest common factor, since the greatest common factor cannot be larger than the smaller of the two numbers.

But, we can also look at a factorization of both numbers.

We can tell that 3y2 = 3 x y2.

We can tell that 24y3 = 3 x 8 x y3 = 3 x 23 x y2 x y.

These numbers have in common 3 and y2, so 3y2 is the greatest common factor.

To round to the nearest hundred, you must look at the number that is to the right of the hundreds place. If the number is 5 or higher, then you round up to the next highest number. If the number is 4 or lower, then you must round down. For example, if you had the number 560, you would round that up because the number to the right of the hundreds place is 6. 560 rounded to the nearest hundred is 600. Another example is 420. You would round 420 down because the number that is the right of the hundreds place is 2. 420 rounded to the nearest hundred is 400.

11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583, 594, 605, 616, 627, 638, 649, 660, 671, 682, 693, 704, 715, 726, 737, 748, 759, 770, 781, 792, 803, 814, 825, 836, 847, 858, 869, 880, 891, 902, 913, 924, 935, 946, 957, 968, 979, and 990!!

The greatest common factor of 18, 27, and 36 is 9

The prime factorization of 18 is 2*3*3

The prime factorization of 27 is 3*3*3

The prime factorization of 36 is 2*2*3*3

The GCF is 3*3 = 9.

The highest common factor of two numbers is the largest number that can evenly divide both numbers. To find the highest common factor of 200 and 350, we need to find the common factors of both numbers and determine the largest one. The factors of 200 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, and 200, while the factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, and 350. The highest common factor of 200 and 350 is 50.

The lowest common multiple of 900 and 270 is the smallest number that is a multiple of both 900 and 270. To find the lowest common multiple, you need to first find the prime factors of each number. The prime factors of 900 are 2^2 * 3^2 * 5^2, and the prime factors of 270 are 2 * 3^3 * 5. To find the lowest common multiple, you take the highest power of each prime factor that appears in either number, which gives you 2^2 * 3^3 * 5^2 = 5400. Therefore, the lowest common multiple of 900 and 270 is 5400.

To find the Least Common Multiple (LCM) of 45, 75, and 90, we first need to find the prime factorization of each number.

45 = 3 x 3 x 5 75 = 3 x 5 x 5 90 = 2 x 3 x 3 x 5

Next, we identify the highest power of each prime factor that appears in any of the factorizations. The LCM is then calculated by multiplying these highest powers together.

Therefore, the LCM of 45, 75, and 90 is 2 x 3^2 x 5^2 = 450.

The factors of 180 are:

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180

The factors of 252 are:

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252