Q: What are the factor combinations of the number 13,028,225?

 A:
Positive:   1 x 130282255 x 26056457 x 186117525 x 52112935 x 372235109 x 119525175 x 74447545 x 23905683 x 19075763 x 170752725 x 47813415 x 3815
Negative: -1 x -13028225-5 x -2605645-7 x -1861175-25 x -521129-35 x -372235-109 x -119525-175 x -74447-545 x -23905-683 x -19075-763 x -17075-2725 x -4781-3415 x -3815


How do I find the factor combinations of the number 13,028,225?

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 13,028,225, 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 13,028,225
-1 -13,028,225

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 13,028,225.

Example:
1 x 13,028,225 = 13,028,225
and
-1 x -13,028,225 = 13,028,225
Notice both answers equal 13,028,225

With that explanation out of the way, let's continue. Next, we take the number 13,028,225 and divide it by 2:

13,028,225 ÷ 2 = 6,514,112.5

If the quotient is a whole number, then 2 and 6,514,112.5 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 13,028,225
-1 -13,028,225

Now, we try dividing 13,028,225 by 3:

13,028,225 ÷ 3 = 4,342,741.6667

If the quotient is a whole number, then 3 and 4,342,741.6667 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 13,028,225
-1 -13,028,225

Let's try dividing by 4:

13,028,225 ÷ 4 = 3,257,056.25

If the quotient is a whole number, then 4 and 3,257,056.25 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 13,028,225
-1 13,028,225
Keep dividing by the next highest number until you cannot divide anymore.

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

15725351091755456837632,7253,4153,8154,78117,07519,07523,90574,447119,525372,235521,1291,861,1752,605,64513,028,225
-1-5-7-25-35-109-175-545-683-763-2,725-3,415-3,815-4,781-17,075-19,075-23,905-74,447-119,525-372,235-521,129-1,861,175-2,605,645-13,028,225

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