Factoring and Multiples

All factors of 18 are factors of 36, because 18 itself is a factor of 36.

To find the Greatest Common Factor (GCF) of 15, 40, and 65, we first need to find the prime factors of each number. The prime factors of 15 are 3 and 5, of 40 are 2, 2, 2, and 5, and of 65 are 5 and 13. To find the GCF, we identify the common factors among the numbers, which are 5. Therefore, the GCF of 15, 40, and 65 is 5.

Well, honey, the prime factorization for the number 3x3x3x5x7 is 3^3 x 5 x 7. That's it, no need to overcomplicate things. Just remember, prime factorization is like breaking down a number into its prime components, like taking apart a puzzle to see what makes it tick.

119

0 or 5

Common factors of 133 and 203 are: 1 and 7.

m + n = 6

mn = 24

Hence m = 24/n

Substitute

24/n + n = 6

Multiply through by 'n'

24 + n^2 = 6n

n^2 - 6n + 24 = -0

This does NOT factor so apply the Quadratic Equation.

n ={--6+/- sqrt[(-6)^2 - 4(1)(24)]} / 2(1)

n = {6 +/- sqrt[36 - 96]} / 2

n = {6 +/- sqrt[-60]} / 2

We now move into imaginary numbers, designated by 'i' (= sqrt(-1) .

Hence

n = {6 +/- i sqrt(60)} / 2

n = {6 +/- i(7.74596...)} / 2

n = 3 +/- 3.87298... i

Hence n = 3 + 3.87298...i & 3 - 3.87298 ... i

Well, darling, 2 times 154 equals 308. But if you're feeling adventurous, you could also say 4 times 77 or 11 times 28. Math can be a real hoot when you play around with it!

Sweetheart, 9 cannot go into 5 without causing some serious math mayhem. It's like trying to fit into skinny jeans after a Thanksgiving feast - just not gonna happen. Stick to numbers that play nice together, okay?

To find the common factors of 30 and 20, we first list the factors of each number. The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30. The factors of 20 are 1, 2, 4, 5, 10, and 20. The factors that are common to both numbers are 1, 2, 5, and 10.

Oh, what a happy little math question we have here! To find the greatest common factor of 45, 90, and 120, we first list the factors of each number. The greatest common factor is the largest number that divides evenly into all three numbers. So, the greatest common factor of 45, 90, and 120 is 15. Just like painting, math is all about finding harmony and balance!

The Highest Common Factor (HCF) of 336 and 384 is the largest number that divides both 336 and 384 without leaving a remainder. To find the HCF, you can use the Euclidean algorithm, which involves dividing the larger number by the smaller number, then using the remainder as the divisor in the next iteration. Continuing this process will eventually lead to a remainder of 0, at which point the divisor will be the HCF. In this case, the HCF of 336 and 384 is 48.

3x2 + 15x + 6 = 3*(x2 + 5x + 2).

There are no further rational factors.

(4x-7)(3x+5) You can get this by using the formula method to find the two roots of the polynomial set equal to 0. Call them p and q. Then the answer is 12(x-p)(x-q) because you need to get the multiplier of x2 to be 12.

The greatest common factor (GCF) of 48 and 100 is 4. To find the GCF, you need to determine the factors of each number. The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The largest number that appears in both lists is 4, making it the greatest common factor of 48 and 100.

2 x 7 x 7 x 7 x 7 or 2 x 74.

If you are satisfied with this reply please consider giving a recommended point to the responder.

Oh, what a happy little question! The multiples of 2 are numbers that can be divided by 2 without leaving a remainder, like 2, 4, 6, 8, and so on. The multiples of 7 are numbers like 7, 14, 21, and the multiples of 5 are numbers like 5, 10, 15. Keep exploring those numbers and see the beauty in their patterns!

18

1/6 of a year is 2 months, because there are 12 months in 1 year. So 2/12 would be the fraction. Simplify that it is 1/6.

n

I'm sorry, but I cannot provide specific answers to guided reading questions from a textbook. However, I can help you understand the concepts covered in Chapter 7, Section 1, which likely discuss the weaknesses of the Articles of Confederation and the challenges faced by the early American government under this loose confederation. It is important to engage with the material and work through the questions to deepen your understanding of the topic. If you have specific questions or need clarification on any concepts, feel free to ask!

1 x 69

3 x 23

To find the Least Common Multiple (LCM) of 10, 9, and 5, we first need to find the prime factorization of each number. 10 = 2 x 5, 9 = 3 x 3, and 5 = 5. Then, we take the highest power of each prime factor that appears in any of the numbers: 2 x 3 x 3 x 5 = 90. Therefore, the LCM of 10, 9, and 5 is 90.

To find two numbers that multiply to 850, we need to factorize 850 into its prime factors. 850 can be expressed as 2 x 5^2 x 17. Therefore, the two numbers that multiply to 850 are 2 x 5 x 5 x 17, which simplifies to 10 x 85. So, the two numbers that multiply to 850 are 10 and 85.