Q: What are the factor combinations of the number 1,253,309?

 A:
Positive:   1 x 1253309101 x 12409
Negative: -1 x -1253309-101 x -12409


How do I find the factor combinations of the number 1,253,309?

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 1,253,309, 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 1,253,309
-1 -1,253,309

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 1,253,309.

Example:
1 x 1,253,309 = 1,253,309
and
-1 x -1,253,309 = 1,253,309
Notice both answers equal 1,253,309

With that explanation out of the way, let's continue. Next, we take the number 1,253,309 and divide it by 2:

1,253,309 ÷ 2 = 626,654.5

If the quotient is a whole number, then 2 and 626,654.5 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 1,253,309
-1 -1,253,309

Now, we try dividing 1,253,309 by 3:

1,253,309 ÷ 3 = 417,769.6667

If the quotient is a whole number, then 3 and 417,769.6667 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 1,253,309
-1 -1,253,309

Let's try dividing by 4:

1,253,309 ÷ 4 = 313,327.25

If the quotient is a whole number, then 4 and 313,327.25 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 1,253,309
-1 1,253,309
Keep dividing by the next highest number until you cannot divide anymore.

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

110112,4091,253,309
-1-101-12,409-1,253,309

More Examples

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