# Factoring and Multiples

## This category should include questions about greatest common factors and lowest common multiples.

### What are the factors of 36? The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factor pairs of 36 are 1 x 36, 2 x 18, 3 x 12, 4 x 9, and 6 x 6. The prime factors of 36 are 2 x 2 x 3 x 3. The distinct prime factors of 36 are 2 and 3. Factors of 36 = 2 X 2 X3 X 3. It can also be written as 4 X 9 and 18 X 2 and 6 x6 and 12 X3 . 1,2,4,6,7,9,12,19,20,9,20,26

### What are the factors of 50? The factors of 50 are 1, 2, 5, 10, 25, and 50 because each of those whole numbers, and no others, divides evenly (with no remainder) into 50. 1,2,5,10,25,50 The factors of 50 are 1, 2, 5, 10, 25, and 50. 1, 2, 5, 10, 25, 50. 1 2 5 10 25 50

### What is range mean in math? Here's what you do you find the smallest number and the larger number then subtract. For EXAMPLE: 12,18,22,24,25,32 32-12=20 so your RANGE is 20. The possible x values of a function.

### What are the shared prime factors of 36 and 144? 2 and 3. In fact, 2 and 3 are the ONLY prime factors of both. 36 = 22 x 32. 144 = 24 x 32.

### What are the factors of 45? The factors of 45 are 1, 3, 5, 9, 15 and 45. The factor pairs of 45 are 1 x 45, 3 x 15, and 5 x 9

### What are the factors of 24? The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, and 24 The factor pairs of 24 are 1 x 24, 2 x 12, 3 x 8, and 4 x 6 The prime factorization of 24 = 2 x 2 x 2 x 3 = 2³ × 3 They are: 1 2 3 4 6 8 12 and 24 The factor of 24 are: 1,2,3,4,6,8,12,24

### What are the factors of 20? The factors of 20 are 1, 2, 4, 5, 10, and 20. 1, 2, 4, 5, 10, 20 1, 2, 4, 5, 10, 20. Its factors are: 1 2 4 5 10 and 20

### What two numbers add to be 6 and multiply to be negative 495? Mathematically, you are looking to answer the following system of equations: x + y = 6 x * y = -495 This is rather simple. First, determine x in terms of y: x = 6 - y Next, substitute for x in the second equation: (6 - y) * y = -495 Now, solve for y: 6y - y2 = - 495 0 = y2 - 6y - 495 The solution to the above quadratic equation is: y = (6 + sqrt(2016)) / 2 and y = (6 - sqrt(2016)) / 2 reducing that further gives y = 3+6*sqrt(14) or 3-6*sqrt(14) Substituting back in to x=6-y, that means: x = 3-6*sqrt(14) when y = 3+6*sqrt(14) x = 3+6*sqrt(14) when y = 3-6*sqr(14) Thus, the two numbers that satisfy your question are: 3+6*sqrt(14) or approximately 25.449944 and 3-6*sqrt(14) or approximately -19.449944

### How do you factor the trinomial 6x2 - 13x - 63? 6x2 - 13x - 63 = (2x - 9)(3x + 7). 6x2 - 13x - 63 since (6)(-63) = -(2*3*9*7) = (-27)(14),then -27 + 14 = -13, I write: = (6x - 27)(6x + 14)/3*2 = (2x - 9)(3x + 7)

### How do you factorise 2a plus 4b plus 8c? 2a + 4b + 8c = 2(a + 2b + 4c) You could also continue by factoring the inside of the parentheses a bit: 2a + 4b + 8c = 2(a + 2b + 4c) = 2(a + 2[b + 2c])

### What is the prime factorization of one billion using exponents? 1 billion {short scale} = 109 = (2*5)9 = 29 * 59 [see related link for short scale and long scale for billion]

### How is a unit rate calculated? for example, if the question is 24 pineapples per 3 waffles, you divide 24 by 3 and you get 8 pineapples per waffle(the mathematical-ish way to write that is 24 pineapples/waffle.).

### What is the least common multiple of 18 and 35? Factor out each term: 18 = 3 x 6 = 3 x 3 x 2 = 2 x 3² 35 = 5 x 7 Since these terms don't have a common factor, we can multiply all these primes altogether to obtain: 2 x 3² x 5 x 7 = 18 x 35 = 630

### Does a factor have to be a whole number? If you are thinking of prime factorization of integers, yes, a prime number more specifically

### What are the factors of 60? The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The factor pairs of 60 are: 1x60 = 60 2x30 = 60 3x20 = 60 4x15 = 60 5x12 = 60 6x10 = 60 The prime factors of 60 are: 2, 2, 3, and 5. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

### What are the Greatest common factor of 63 and 147? One method is to express each number in terms of its prime factors. 63 = 3 x 3 x 7 = 32 x 7. 147 = 3 x 7 x 7 = 3 x 72. The factors that both numbers have in common are 3 and 7. The Greatest Common Factor (GCF) is 3 x 7 = 21.