Factoring and Multiples

The greatest common factor (GCF) of 10, 35, and 110 is 5. To find the GCF, you need to determine the factors of each number and then identify the largest factor that is common to all three numbers. The factors of 10 are 1, 2, 5, and 10. The factors of 35 are 1, 5, 7, and 35. The factors of 110 are 1, 2, 5, 10, 11, 22, 55, and 110. The largest factor that is common to all three numbers is 5, making it the greatest common factor.

That's easy :) 12

1 x 612, 2 x 306, 3 x 204, 4 x 153, 6 x 102, 9 x 68, 12 x 51, 17 x 36, 18 x 34 = 612

Oh, dude, you're hitting me with some math? Alright, so the common factors of 128 and 96 are 1, 2, 4, 8, and 16. Basically, they're like the friends that both 128 and 96 hang out with, you know? They can all divide both numbers without any drama.

The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the two numbers with an LCM of 1260, we need to factorize 1260 into its prime factors, which are 2, 2, 3, 3, 5, and 7. We then pair these prime factors to form two numbers, such as 2 x 2 x 3 x 5 = 60 and 3 x 7 = 21. Therefore, the two numbers with an LCM of 1260 are 60 and 21.

24 it has 1, 2, 3, 4, 6, 8, 12, and 24... that's 8 numbers.

To determine the value of the expression x-a x-b x-c x-z, we need to consider the factors of the expression. Since each letter of the alphabet (excluding x) is subtracted from x in one of the factors, there are a total of 26 factors. This means that the expression must be expanded to include all 26 letters of the alphabet as factors, resulting in x-a x-b x-c ... x-z. Therefore, the value of the expression is x-a x-b x-c ... x-z.

The Highest Common Factor (HCF) of 200 and 300 is the largest number that divides both 200 and 300 without leaving a remainder. To find the HCF, you can factorize both numbers: 200 = 2 x 2 x 2 x 5 x 5 and 300 = 2 x 2 x 3 x 5 x 5. Then, identify the common prime factors and multiply them: HCF = 2 x 2 x 5 = 20. Therefore, the HCF of 200 and 300 is 20.

Oh, dude, that's like 540. You've got your 2s, your 3s, and your 5 all multiplied together. It's like a prime factorization party up in here.

To write 9614 in expanded form using exponents, we break down the number into its place values. 9614 can be expressed as (9 x 10^3) + (6 x 10^2) + (1 x 10^1) + (4 x 10^0). This means that 9614 is equal to 9 thousands, 6 hundreds, 1 ten, and 4 ones.

The GCF is 5.

Oh, dude, you're asking about multiples of 224? Alright, like, multiples are just numbers you can multiply to get 224, so it's like 1, 2, 4, 7, 8, 14, 16, 28, 56, 112, and 224. There you go, a bunch of numbers that can hang out with 224 and call themselves multiples.

To find two numbers that multiply to 32 and add up to 8, we can set up a system of equations. Let's call the two numbers x and y. From the given conditions, we have xy = 32 and x + y = 8. By solving these equations simultaneously, we can find the two numbers. The solution is 4 and 8, as 4 * 8 = 32 and 4 + 8 = 8.

Oh, isn't that a happy little question! To find out what times what equals 8.4, we can think of it as a little math adventure. If we take a stroll with our paintbrush and canvas, we'll find that 2.1 times 4 equals 8.4. Just like painting a beautiful landscape, sometimes all we need is a little patience and a gentle touch to uncover the answer.

The GCF is 5.

Well, sweetheart, 4 and 8 can both go into numbers that are multiples of both 4 and 8. In other words, they can both go into numbers that are divisible by both 4 and 8. So, grab your calculator and start crunching those numbers!

Oh, what a happy little question! To find the highest common factor of 84, 98, and 168, we can first find the factors of each number. Then, we look for the largest number that divides evenly into all three. Let's paint a beautiful picture together as we discover that the highest common factor of 84, 98, and 168 is 14.

30: 1, 2, 3, 5, 6, 10, 15, 30 45: 1, 3, 5, 9, 15, 45 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 105: 1, 3, 5, 7, 15, 21, 35 Therefore, the greatest common factor(GCF) of them is 15.

gcf(304560 105) = 15

Found by prime factorisation:

304560 = 2^4 x 3^4 x 5 x 47

105 = 3 x 5 x 7

hcf = 3 x 5 = 15

However, I suspect that you asked for the gcf of 30,45,60 and 105 and the commas were stripped (as they cause problems with accessing questions across the internet - putting a space after the comma would have left the numbers readable), in which case:

gcf(30, 45, 60, 105) = 15

Found by prime factorization:

30 = 2 x 3 x 5

45 = 3^2 x 5

60 = 2^2 x 3 x 5

105 = 3 x 5 x 7

hcf = 3 x 5 = 15

[Curiously the hcf is the same in both cases.)

Well, isn't that just a happy little math question! To find the Greatest Common Factor (GCF) of 34, 85, and 102, we can start by finding the factors of each number. The GCF is the largest number that divides evenly into each of the numbers, so let's explore those factors and find the common one that brings harmony to these numbers. Just like adding colors to a painting, we'll find the common factor that brings these numbers together beautifully.

The GCF/HCF of 95 and 185 is 5.

The greatest common factor (GCF) of 108, 72, and 144 is 36. To find the GCF, you need to identify the common factors of the numbers and determine the largest one they all share. In this case, the common factors of 108, 72, and 144 are 1, 2, 3, 4, 6, 9, 12, 18, 36, with 36 being the greatest.

288 is a composite number because it has factors other than 1 and itself. It is not a prime number.

The 18 factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, and 288.

The factor pairs of 288 are 1 x 288, 2 x 144, 3 x 96, 4 x 72, 6 x 48, 8 x 36, 9 x 32, 12 x 24, and 16 x 18.

The proper factors of 288 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, and 144 or,
if the definition you are using excludes 1, they are 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, and 144.

The prime factors of 288 are 2, 2, 2, 2, 2, 3, and 3. Note: There is repetition of these factors, so if the prime factors are being listed instead of the prime factorization, usually only the distinct prime factors are listed.

The distinct prime factors of 288 are 2 and 3.

The prime factorization of 288 is 2 x 2 x 2 x 2 x 2 x 3 x 3 or, in exponential form, 25 x 32.

To find the GCF of any set of numbers.

Divide the numbers by their prime number factors, and see which is common to each number in the set.

Hence 160,240 & 200.

160 = 2x2x2x2'x2'x5

200 = 2x2x2x5'x5

240 = 2x2x2x2'x3'x5

So each number has 2x2x2x5 (common to all three numbers)

2x2x2x5 = 40 The GCF.

NB THe other factors are discrete to the given number. So for 200 the second '5' is discrete to 200 and so is not common to all the other numbers.

I have written the discrete numbers as (2') etc.,

33 and 39

The way to do this is to see which odd numbers between 30 and 40 have digits that add up to a multiple of 3 since this is the test to see if a number is divisible by 3.
So 33 has digits that add to 6 since 3+3=6 and 33 is odd
Also, 39 has digits that add up to 12 since 3+=12 and 39 is odd.


36 has digits that add to 9, but it is even so we discard it.