Q: What are the factor combinations of the number 13,240,409?

 A:
Positive:   1 x 132404097 x 189148713 x 101849383 x 15952391 x 145499581 x 227891079 x 122711753 x 7553
Negative: -1 x -13240409-7 x -1891487-13 x -1018493-83 x -159523-91 x -145499-581 x -22789-1079 x -12271-1753 x -7553


How do I find the factor combinations of the number 13,240,409?

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 13,240,409, 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 13,240,409
-1 -13,240,409

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 13,240,409.

Example:
1 x 13,240,409 = 13,240,409
and
-1 x -13,240,409 = 13,240,409
Notice both answers equal 13,240,409

With that explanation out of the way, let's continue. Next, we take the number 13,240,409 and divide it by 2:

13,240,409 ÷ 2 = 6,620,204.5

If the quotient is a whole number, then 2 and 6,620,204.5 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 13,240,409
-1 -13,240,409

Now, we try dividing 13,240,409 by 3:

13,240,409 ÷ 3 = 4,413,469.6667

If the quotient is a whole number, then 3 and 4,413,469.6667 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 13,240,409
-1 -13,240,409

Let's try dividing by 4:

13,240,409 ÷ 4 = 3,310,102.25

If the quotient is a whole number, then 4 and 3,310,102.25 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 13,240,409
-1 13,240,409
Keep dividing by the next highest number until you cannot divide anymore.

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

171383915811,0791,7537,55312,27122,789145,499159,5231,018,4931,891,48713,240,409
-1-7-13-83-91-581-1,079-1,753-7,553-12,271-22,789-145,499-159,523-1,018,493-1,891,487-13,240,409

More Examples

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