# Factoring and Multiples

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

###### Asked in Factoring and 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

###### Asked in Math and Arithmetic, Algebra, Factoring and Multiples

### 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