Q: What are the factor combinations of the number 25,178,321?

 A:
Positive:   1 x 251783217 x 3596903113 x 222817139 x 181139229 x 109949791 x 31831973 x 258771603 x 15707
Negative: -1 x -25178321-7 x -3596903-113 x -222817-139 x -181139-229 x -109949-791 x -31831-973 x -25877-1603 x -15707


How do I find the factor combinations of the number 25,178,321?

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 25,178,321, 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 25,178,321
-1 -25,178,321

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 25,178,321.

Example:
1 x 25,178,321 = 25,178,321
and
-1 x -25,178,321 = 25,178,321
Notice both answers equal 25,178,321

With that explanation out of the way, let's continue. Next, we take the number 25,178,321 and divide it by 2:

25,178,321 ÷ 2 = 12,589,160.5

If the quotient is a whole number, then 2 and 12,589,160.5 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 25,178,321
-1 -25,178,321

Now, we try dividing 25,178,321 by 3:

25,178,321 ÷ 3 = 8,392,773.6667

If the quotient is a whole number, then 3 and 8,392,773.6667 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 25,178,321
-1 -25,178,321

Let's try dividing by 4:

25,178,321 ÷ 4 = 6,294,580.25

If the quotient is a whole number, then 4 and 6,294,580.25 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 25,178,321
-1 25,178,321
Keep dividing by the next highest number until you cannot divide anymore.

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

171131392297919731,60315,70725,87731,831109,949181,139222,8173,596,90325,178,321
-1-7-113-139-229-791-973-1,603-15,707-25,877-31,831-109,949-181,139-222,817-3,596,903-25,178,321

More Examples

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