Q: What are the factor combinations of the number 10,321,625?

 A:
Positive:   1 x 103216255 x 206432525 x 41286571 x 145375125 x 82573355 x 290751163 x 88751775 x 5815
Negative: -1 x -10321625-5 x -2064325-25 x -412865-71 x -145375-125 x -82573-355 x -29075-1163 x -8875-1775 x -5815


How do I find the factor combinations of the number 10,321,625?

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 10,321,625, 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 10,321,625
-1 -10,321,625

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 10,321,625.

Example:
1 x 10,321,625 = 10,321,625
and
-1 x -10,321,625 = 10,321,625
Notice both answers equal 10,321,625

With that explanation out of the way, let's continue. Next, we take the number 10,321,625 and divide it by 2:

10,321,625 ÷ 2 = 5,160,812.5

If the quotient is a whole number, then 2 and 5,160,812.5 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 10,321,625
-1 -10,321,625

Now, we try dividing 10,321,625 by 3:

10,321,625 ÷ 3 = 3,440,541.6667

If the quotient is a whole number, then 3 and 3,440,541.6667 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 10,321,625
-1 -10,321,625

Let's try dividing by 4:

10,321,625 ÷ 4 = 2,580,406.25

If the quotient is a whole number, then 4 and 2,580,406.25 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 10,321,625
-1 10,321,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1525711253551,1631,7755,8158,87529,07582,573145,375412,8652,064,32510,321,625
-1-5-25-71-125-355-1,163-1,775-5,815-8,875-29,075-82,573-145,375-412,865-2,064,325-10,321,625

More Examples

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