Factoring and Multiples

Oh, dude, the greatest common factor of 40 and 54 is 2. Yeah, like, you can totally break down 40 into 2 x 2 x 2 x 5 and 54 into 2 x 3 x 3 x 3, and then you just pick out the common factors. Voilà, you've got your answer!

The greatest common factor (GCF) of 3x and 6 is 3. To factor out the GCF, you divide each term by the GCF. So, 3x ÷ 3 = x and 6 ÷ 3 = 2. Therefore, the factored out GCF of 3x and 6 is 3(x + 2).

The factors of 30 are:

1, 2, 3, 5, 6, 10, 15, 30

The factors of 210 are:

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

The factors of 700 are:

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

The factors of 30210 are:

1, 2, 3, 5, 6, 10, 15, 19, 30, 38, 53, 57, 95, 106, 114, 159, 190, 265, 285, 318, 530, 570, 795, 1007, 1590, 2014, 3021, 5035, 6042, 10070, 15105, 30210

Oh, what a happy little question we have here! To find the factors of 18xy, we need to break it down into its smallest parts. The factors of 18 are 1, 2, 3, 6, 9, and 18, while the factors of x and y are just x and y themselves. So, the factors of 18xy are 1, 2, 3, 6, 9, 18, x, y, 2x, 3x, 6x, 9x, 18x, xy, 2y, 3y, 6y, 9y, and 18y.

729×1

Oh, what a happy little question! The number that has factors of both 12346 and 12 is 12346, as it includes both sets of factors. It's like mixing different colors on your palette to create a beautiful painting - each number brings its own unique contribution to the final result. Just remember, there are no mistakes in math, only happy little accidents!

Oh, isn't that a happy little question! To find the Greatest Common Factor (GCF) of 32 and 90, we can list the factors of each number. The factors of 32 are 1, 2, 4, 8, 16, and 32, and the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. The largest number that appears in both lists is 2, so the GCF of 32 and 90 is 2.

Well, darling, the greatest common factor of 32 and 9 is 1. Those two numbers don't have any common factors other than 1 because they're as different as night and day. So, there you have it - the sassy truth!

There are some multiples of 15 from 15 to 500! Here it is...

15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, 330, 345, 360, 375, 390, 405, 420, 435, 450, 465, 480, 495

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

Also me: HuMaN calculator.

To find the greatest common factor of 60 and 210, you first need to list the factors of each number. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210. The greatest common factor is the largest number that appears in both lists, which in this case 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.

Oh, dude, 6 can be divided by 1, 2, 3, and 6. It's like the popular kid at the division party, everyone wants a piece of that 6 action. So yeah, those are the lucky numbers that can divide 6 without any drama.

1 x 215, 5 x 43

Zero has an infinite number of factors. This is because any number multiplied by zero equals zero, so all integers are factors of zero. In other words, zero is divisible by any non-zero integer, making its list of factors endless.

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.