# How do you know when you have found a solution to the equation 3y + x = 12?

## Answers

idkk ask google , google knows

One method of finding the factors of a number is to perform a divisibility test on it, using the results to find pairs of factors. If you use this method, you know you've found all of the factors when you start going back towards factors you found at the beginning.

Example:

Take 84. We know that 1 is a factor of every number, and 1 goes into it 84 times, so 1 and 84 are factors.

Since it is even, 84 is divisible by 2. 84/2 = 42, so 2 and 42 are factors.

To test for divisibility by 3, add the digits together: 8+4=12. Since 12 is divisible by 3, 84 is also divisible by 3. 84/3 = 28, so 3 and 28 are factors.

4 will divide into 8 and 4 will divide into 4, so 84 is divisible by 4. 84/4 = 21, so 4 and 21 are factors.

84 does not end in 5 or 0, so it is not divisible by 5.

Since it is divisible by both 2 and 3, 84 is divisible by 6. 84/6 = 14, so 6 and 14 are factors.

84 is divisible by 7; 84/7 = 12, so 7 and 12 are factors.

84 is not divisible by 8.

To check for divisibility by 9, look at the sum of the digits again. 8+4 = 12; 12 is not divisible by 9, so neither is 84.

Since the number does not end in 0, 84 is not divisible by 10.

84 is not divisible by 11.

We already know that 84 is divisible by 12 (84/7 = 12); since we've come across one we've seen before, we know we are finished.

The last factor will usually be the number itself. Like for example the factors of 15 are 1,3,5,15. I know those are the only numbers because it ended with 15 .

When the number is reduced to its lowest point

When you cant simplyfy it anymore

When you come to a number that you can't divide any more

When you end up with prime numbers for example

If you factored out 12 you could say 3x4. Now 3 is a prime number so it cant be broken down any more. You can break down 4 into 2x2. 2 is a prime number so cant be broken down any further. When 12 is factored out it is 2x2x3

You know because all the factors are prime, none of them are one, and they multiply to make said number.

Hope this helps :)

You will know you have all the factors when you have the last factor as the number

You wont be able to break it down/ simplify it