Q: What are the factor combinations of the number 13,140,125?

 A:
Positive:   1 x 131401255 x 262802525 x 52560531 x 423875125 x 105121155 x 84775775 x 169553391 x 3875
Negative: -1 x -13140125-5 x -2628025-25 x -525605-31 x -423875-125 x -105121-155 x -84775-775 x -16955-3391 x -3875


How do I find the factor combinations of the number 13,140,125?

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 13,140,125, 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 13,140,125
-1 -13,140,125

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 13,140,125.

Example:
1 x 13,140,125 = 13,140,125
and
-1 x -13,140,125 = 13,140,125
Notice both answers equal 13,140,125

With that explanation out of the way, let's continue. Next, we take the number 13,140,125 and divide it by 2:

13,140,125 ÷ 2 = 6,570,062.5

If the quotient is a whole number, then 2 and 6,570,062.5 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 13,140,125
-1 -13,140,125

Now, we try dividing 13,140,125 by 3:

13,140,125 ÷ 3 = 4,380,041.6667

If the quotient is a whole number, then 3 and 4,380,041.6667 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 13,140,125
-1 -13,140,125

Let's try dividing by 4:

13,140,125 ÷ 4 = 3,285,031.25

If the quotient is a whole number, then 4 and 3,285,031.25 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 13,140,125
-1 13,140,125
Keep dividing by the next highest number until you cannot divide anymore.

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

1525311251557753,3913,87516,95584,775105,121423,875525,6052,628,02513,140,125
-1-5-25-31-125-155-775-3,391-3,875-16,955-84,775-105,121-423,875-525,605-2,628,025-13,140,125

More Examples

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