Q: What are the factor combinations of the number 25,690,165?

 A:
Positive:   1 x 256901655 x 513803331 x 828715107 x 240095155 x 165743535 x 480191549 x 165853317 x 7745
Negative: -1 x -25690165-5 x -5138033-31 x -828715-107 x -240095-155 x -165743-535 x -48019-1549 x -16585-3317 x -7745


How do I find the factor combinations of the number 25,690,165?

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 25,690,165, 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 25,690,165
-1 -25,690,165

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 25,690,165.

Example:
1 x 25,690,165 = 25,690,165
and
-1 x -25,690,165 = 25,690,165
Notice both answers equal 25,690,165

With that explanation out of the way, let's continue. Next, we take the number 25,690,165 and divide it by 2:

25,690,165 ÷ 2 = 12,845,082.5

If the quotient is a whole number, then 2 and 12,845,082.5 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 25,690,165
-1 -25,690,165

Now, we try dividing 25,690,165 by 3:

25,690,165 ÷ 3 = 8,563,388.3333

If the quotient is a whole number, then 3 and 8,563,388.3333 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 25,690,165
-1 -25,690,165

Let's try dividing by 4:

25,690,165 ÷ 4 = 6,422,541.25

If the quotient is a whole number, then 4 and 6,422,541.25 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 25,690,165
-1 25,690,165
Keep dividing by the next highest number until you cannot divide anymore.

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

15311071555351,5493,3177,74516,58548,019165,743240,095828,7155,138,03325,690,165
-1-5-31-107-155-535-1,549-3,317-7,745-16,585-48,019-165,743-240,095-828,715-5,138,033-25,690,165

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