Q: What are the factor combinations of the number 361,229?

 A:
Positive:   1 x 36122911 x 32839
Negative: -1 x -361229-11 x -32839


How do I find the factor combinations of the number 361,229?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 361,229, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 361,229
-1 -361,229

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 361,229.

Example:
1 x 361,229 = 361,229
and
-1 x -361,229 = 361,229
Notice both answers equal 361,229

With that explanation out of the way, let's continue. Next, we take the number 361,229 and divide it by 2:

361,229 ÷ 2 = 180,614.5

If the quotient is a whole number, then 2 and 180,614.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 361,229
-1 -361,229

Now, we try dividing 361,229 by 3:

361,229 ÷ 3 = 120,409.6667

If the quotient is a whole number, then 3 and 120,409.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 361,229
-1 -361,229

Let's try dividing by 4:

361,229 ÷ 4 = 90,307.25

If the quotient is a whole number, then 4 and 90,307.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 361,229
-1 361,229
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

11132,839361,229
-1-11-32,839-361,229

More Examples

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