Q: What are the factor combinations of the number 26,289,025?

 A:
Positive:   1 x 262890255 x 52578057 x 375557525 x 105156135 x 751115175 x 150223
Negative: -1 x -26289025-5 x -5257805-7 x -3755575-25 x -1051561-35 x -751115-175 x -150223


How do I find the factor combinations of the number 26,289,025?

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 26,289,025, 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 26,289,025
-1 -26,289,025

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 26,289,025.

Example:
1 x 26,289,025 = 26,289,025
and
-1 x -26,289,025 = 26,289,025
Notice both answers equal 26,289,025

With that explanation out of the way, let's continue. Next, we take the number 26,289,025 and divide it by 2:

26,289,025 ÷ 2 = 13,144,512.5

If the quotient is a whole number, then 2 and 13,144,512.5 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 26,289,025
-1 -26,289,025

Now, we try dividing 26,289,025 by 3:

26,289,025 ÷ 3 = 8,763,008.3333

If the quotient is a whole number, then 3 and 8,763,008.3333 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 26,289,025
-1 -26,289,025

Let's try dividing by 4:

26,289,025 ÷ 4 = 6,572,256.25

If the quotient is a whole number, then 4 and 6,572,256.25 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 26,289,025
-1 26,289,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1572535175150,223751,1151,051,5613,755,5755,257,80526,289,025
-1-5-7-25-35-175-150,223-751,115-1,051,561-3,755,575-5,257,805-26,289,025

More Examples

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