Q: What are the factor combinations of the number 359,107?

 A:
Positive:   1 x 3591077 x 5130129 x 1238361 x 5887203 x 1769427 x 841
Negative: -1 x -359107-7 x -51301-29 x -12383-61 x -5887-203 x -1769-427 x -841


How do I find the factor combinations of the number 359,107?

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 359,107, 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.

1 359,107
-1 -359,107

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 359,107.

Example:
1 x 359,107 = 359,107
and
-1 x -359,107 = 359,107
Notice both answers equal 359,107

With that explanation out of the way, let's continue. Next, we take the number 359,107 and divide it by 2:

359,107 ÷ 2 = 179,553.5

If the quotient is a whole number, then 2 and 179,553.5 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:

1 359,107
-1 -359,107

Now, we try dividing 359,107 by 3:

359,107 ÷ 3 = 119,702.3333

If the quotient is a whole number, then 3 and 119,702.3333 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:

1 359,107
-1 -359,107

Let's try dividing by 4:

359,107 ÷ 4 = 89,776.75

If the quotient is a whole number, then 4 and 89,776.75 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:

1 359,107
-1 359,107
Keep dividing by the next highest number until you cannot divide anymore.

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

1729612034278411,7695,88712,38351,301359,107
-1-7-29-61-203-427-841-1,769-5,887-12,383-51,301-359,107

More Examples

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