Q: What are the factor combinations of the number 10,902,125?

 A:
Positive:   1 x 109021255 x 218042513 x 83862525 x 43608565 x 167725125 x 87217325 x 335451625 x 6709
Negative: -1 x -10902125-5 x -2180425-13 x -838625-25 x -436085-65 x -167725-125 x -87217-325 x -33545-1625 x -6709


How do I find the factor combinations of the number 10,902,125?

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 10,902,125, 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 10,902,125
-1 -10,902,125

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 10,902,125.

Example:
1 x 10,902,125 = 10,902,125
and
-1 x -10,902,125 = 10,902,125
Notice both answers equal 10,902,125

With that explanation out of the way, let's continue. Next, we take the number 10,902,125 and divide it by 2:

10,902,125 ÷ 2 = 5,451,062.5

If the quotient is a whole number, then 2 and 5,451,062.5 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 10,902,125
-1 -10,902,125

Now, we try dividing 10,902,125 by 3:

10,902,125 ÷ 3 = 3,634,041.6667

If the quotient is a whole number, then 3 and 3,634,041.6667 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 10,902,125
-1 -10,902,125

Let's try dividing by 4:

10,902,125 ÷ 4 = 2,725,531.25

If the quotient is a whole number, then 4 and 2,725,531.25 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 10,902,125
-1 10,902,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151325651253251,6256,70933,54587,217167,725436,085838,6252,180,42510,902,125
-1-5-13-25-65-125-325-1,625-6,709-33,545-87,217-167,725-436,085-838,625-2,180,425-10,902,125

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