Factoring and Multiples

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, darling, the Least Common Multiple (LCM) of 5, 15, and 18 is 90. That's the smallest multiple that all three numbers can divide into without leaving a remainder. So, there you have it, 90 is the magic number in this scenario.

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.

Well, honey, the greatest common factor of 147 and 245 is 49. It's like finding the biggest piece of pie they can both share without fighting over it. So, go ahead and slice up that 49 and serve it with a side of math sass.

The GCF is 4.

To find the greatest common factor (GCF) of 72, 90, and 144, we first need to find the prime factorization of each number. The prime factorization of 72 is 2^3 * 3^2, the prime factorization of 90 is 2 * 3^2 * 5, and the prime factorization of 144 is 2^4 * 3^2. The GCF is the product of the common prime factors raised to the smallest exponent they appear in any of the numbers, which in this case is 2^3 * 3^2, equal to 72.

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, ...

The factors of 3124 are the numbers that can be multiplied together to result in 3124. These factors include 1, 2, 4, 13, 26, 52, 67, 134, 268, 781, 1562, and 3124. Prime factors are the factors that are prime numbers, which means they can only be divided by 1 and themselves. The prime factors of 3124 are 2, 13, and 67.

Sure thing, honey. To write 3624 in expanded form using exponents, you would break it down like this: 3 x 10^3 + 6 x 10^2 + 2 x 10^1 + 4 x 10^0. It's just a fancy way of showing off those digits in a different light.

To find the greatest common factor (GCF) of 549 and 1220, you need to list the factors of each number. The factors of 549 are 1, 3, 7, 61, 183, and 549. The factors of 1220 are 1, 2, 4, 5, 10, 61, 122, 244, 305, 610, and 1220. The GCF is the largest number that appears in both lists, which in this case is 61. Therefore, the GCF of 549 and 1220 is 61.

Oh, dude, a factor tree for 17? That's like finding a needle in a haystack. But hey, here's the deal - 17 is a prime number, so its factor tree would just be 17 hanging out all by itself. It's like the loner at the party who doesn't need anyone else to have a good time.

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!

Well, honey, the factor pairs of 225 are 1 and 225, 3 and 75, 5 and 45, 9 and 25. Those are the pairs you're looking for, darling. Hope that helps!

The numbers that go into 17 are 1 and 17, as 17 is a prime number and only divisible by 1 and itself. The numbers that go into 20 are 1, 2, 4, 5, 10, and 20, as 20 is a composite number with multiple factors.

Well, darling, the LCM of 6, 7, and 18 is 126. It's like finding the least common multiple of a trio of numbers – just multiply the highest power of each prime factor that appears in the numbers. Easy peasy lemon squeezy!

To express 84.95 as a decimal, you would simply write it as 84.95. In decimal form, the whole number part remains the same, and the fractional part remains as is. Therefore, 84.95 as a decimal is 84.95.