Q: What are the factor combinations of the number 356,273?

 A:
Positive:   1 x 35627337 x 9629
Negative: -1 x -356273-37 x -9629


How do I find the factor combinations of the number 356,273?

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 356,273, 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.

1 356,273
-1 -356,273

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 356,273.

Example:
1 x 356,273 = 356,273
and
-1 x -356,273 = 356,273
Notice both answers equal 356,273

With that explanation out of the way, let's continue. Next, we take the number 356,273 and divide it by 2:

356,273 ÷ 2 = 178,136.5

If the quotient is a whole number, then 2 and 178,136.5 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:

1 356,273
-1 -356,273

Now, we try dividing 356,273 by 3:

356,273 ÷ 3 = 118,757.6667

If the quotient is a whole number, then 3 and 118,757.6667 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:

1 356,273
-1 -356,273

Let's try dividing by 4:

356,273 ÷ 4 = 89,068.25

If the quotient is a whole number, then 4 and 89,068.25 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:

1 356,273
-1 356,273
Keep dividing by the next highest number until you cannot divide anymore.

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

1379,629356,273
-1-37-9,629-356,273

More Examples

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