Factoring and Multiples

Oh, dude, the Highest Common Factor (HCF) of 55, 132, and 143 is 11. It's like the cool kid that can divide all these numbers without leaving any remainders. So yeah, 11 is the HCF, no big deal.

Oh, what a happy little question! Well, if we're looking for numbers that can go into 431, we can start by thinking about factors like 1, 7, 61, and 431 itself. Each of these numbers can be multiplied to fit perfectly into 431, just like adding different colors to create a beautiful painting. Remember, there's no mistakes here, just happy little numbers waiting to be discovered.

To find the Greatest Common Factor (GCF) of 27, 63, and 81, we first need to find the prime factors of each number. The prime factorization of 27 is 3 x 3 x 3, the prime factorization of 63 is 3 x 3 x 7, and the prime factorization of 81 is 3 x 3 x 3 x 3. The GCF is the product of the common prime factors raised to the lowest power they appear in any of the numbers, which in this case is 3 x 3 x 3 = 27. Therefore, the GCF of 27, 63, and 81 is 27.

To find the greatest common factor (GCF) of 34, 51, and 102, we first need to find the prime factors of each number. The prime factors of 34 are 2 and 17, the prime factors of 51 are 3 and 17, and the prime factors of 102 are 2, 3, and 17. The GCF is the product of the common prime factors raised to the lowest power, which in this case is 17. Therefore, the GCF of 34, 51, and 102 is 17.

Oh, dude, multiples of 7 up to 5000? Let me casually drop some knowledge on you. So, multiples of 7 are numbers that 7 can be multiplied by to get the number, like 7, 14, 21, and so on. You can find them by just counting by 7s up to 5000. Easy peasy, lemon squeezy.

The common multiples of 6 and 5 are 30, 60, 90, 120, 150, 180, and so on.

Well, isn't that a happy little question! The highest common factor (HCF) of 375 is 75. You see, the HCF is the largest number that divides evenly into both 375 and another number, in this case, 75. Just like painting a beautiful landscape, finding the HCF is all about finding the common threads that bring everything together in harmony.

To express 75 as a product of its prime factors, we first determine its prime factors. 75 = 3 x 25, and 25 = 5 x 5. Therefore, the prime factors of 75 are 3, 5, and 5. Thus, 75 can be expressed as a product of its prime factors as 3 x 5 x 5, or 3 x 5^2.

Oh, dude, the greatest common factor of 147 and 245 is 49. It's like when you're trying to find the one thing they both have in common, and it's just 49, you know? So, if you ever need to divide both 147 and 245 by something, 49's got your back.

The GCF is 4.

LCM of 28 40 & 144 is 5040.

Oh, dude, let's break out the math hats for this one. The greatest common factor of 1325 and 3498 is 1. Yeah, just 1. They don't have any other factors in common. It's like they're distant math cousins who just don't have much in common, you know?

11158 ÷ 77 = 144 r 70

Thus an extra 77 - 70 = 7 needs to be added to make it divisible by 77. A further 77 can also be added which will still result in a multiple of 77, ie adding 84 will also result in a multiple of 77. Thus the one "of the following" to add is the one which is one of:

7, 84, 161, 238, 315, 392, 469, 546, 623, 700, 777, 854, 931, 1008, 1085, 1162, 1239, 1316, 1393, 1470, 1547, 1624, 1701, 1778, 1855, 1932, 2009, 2086, 2163, 2240, 2317, 2394, 2471, 2548, 2625, 2702, 2779, 2856, 2933, 3010, 3087, 3164, 3241, 3318, 3395, 3472, 3549, 3626, 3703, 3780, 3857, 3934, 4011, 4088, 4165, 4242, 4319, 4396, 4473, 4550, 4627, 4704, 4781, 4858, 4935, 5012, 5089, 5166, 5243, 5320, 5397, 5474, 5551, 5628, 5705, 5782, 5859, 5936, 6013, 6090, 6167, 6244, 6321, 6398, 6475, 6552, 6629, 6706, 6783, 6860, 6937, 7014, 7091, 7168, 7245, 7322, 7399, 7476, 7553, 7630, 7707, ...

3624 in expanded form is 3000 + 600 +20 +4 translate the expanded form in exponents: 3000= 3* 10 to the power of the 3 600= 6* 10 to the power of 2 20 = 2* 10 to the power of 1 4= 4* 10 to the power of 0

THE GCF of 549 and 1220 is 61.

The factors of 1220 are 1, 2, 4, 5, 10, 20, 61, 122, 244, 305, 610, and 1220

The factors of 549 are 1, 3, 9, 61, 183, and 549

GCF (1220, 549) = 61

Oh honey, a factor tree for 17 is gonna be a short story. It starts with 17, then you realize it's a prime number. So, it's just 17 hanging out by itself, no factors to share the spotlight. Short and sweet, just like me.

1, 2, 4, 5, 10, 20, 25, 50, 100.

The common multiples of 14 and 35 are numbers that are divisible by both 14 and 35. To find the common multiples, we first list the multiples of each number. The multiples of 14 are 14, 28, 42, 56, 70, etc., and the multiples of 35 are 35, 70, 105, 140, etc. The common multiples of 14 and 35 are numbers that appear in both lists, such as 70.

408 can be expressed as the product of its prime factors: 2 x 2 x 2 x 3 x 17. It is also the sum of the first 20 positive even numbers (2 + 4 + 6 + ... + 38 + 40). Additionally, 408 can be represented as the cube of the square root of 6 (6^(1/2))^3.

Oh, dude, prime factors of 45 in index form? That's like asking me to do math on a Friday night. Okay, so 45 can be broken down into 3^2 * 5. There you go, all fancy with the index form and everything. Math wizard over here!

The factor pairs of 225 are 1 x 225, 3 x 75, 5 x 45, 9 x 25, and 15 x 15