Q: What are the factor combinations of the number 10,322,125?

 A:
Positive:   1 x 103221255 x 206442511 x 93837525 x 41288555 x 187675125 x 82577275 x 375351375 x 7507
Negative: -1 x -10322125-5 x -2064425-11 x -938375-25 x -412885-55 x -187675-125 x -82577-275 x -37535-1375 x -7507


How do I find the factor combinations of the number 10,322,125?

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 10,322,125, 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 10,322,125
-1 -10,322,125

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 10,322,125.

Example:
1 x 10,322,125 = 10,322,125
and
-1 x -10,322,125 = 10,322,125
Notice both answers equal 10,322,125

With that explanation out of the way, let's continue. Next, we take the number 10,322,125 and divide it by 2:

10,322,125 ÷ 2 = 5,161,062.5

If the quotient is a whole number, then 2 and 5,161,062.5 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 10,322,125
-1 -10,322,125

Now, we try dividing 10,322,125 by 3:

10,322,125 ÷ 3 = 3,440,708.3333

If the quotient is a whole number, then 3 and 3,440,708.3333 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 10,322,125
-1 -10,322,125

Let's try dividing by 4:

10,322,125 ÷ 4 = 2,580,531.25

If the quotient is a whole number, then 4 and 2,580,531.25 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 10,322,125
-1 10,322,125
Keep dividing by the next highest number until you cannot divide anymore.

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

151125551252751,3757,50737,53582,577187,675412,885938,3752,064,42510,322,125
-1-5-11-25-55-125-275-1,375-7,507-37,535-82,577-187,675-412,885-938,375-2,064,425-10,322,125

More Examples

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