Q: What are the factor combinations of the number 25,531,723?

 A:
Positive:   1 x 255317237 x 364738943 x 593761271 x 94213301 x 84823313 x 815711897 x 134592191 x 11653
Negative: -1 x -25531723-7 x -3647389-43 x -593761-271 x -94213-301 x -84823-313 x -81571-1897 x -13459-2191 x -11653


How do I find the factor combinations of the number 25,531,723?

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 25,531,723, 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 25,531,723
-1 -25,531,723

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 25,531,723.

Example:
1 x 25,531,723 = 25,531,723
and
-1 x -25,531,723 = 25,531,723
Notice both answers equal 25,531,723

With that explanation out of the way, let's continue. Next, we take the number 25,531,723 and divide it by 2:

25,531,723 ÷ 2 = 12,765,861.5

If the quotient is a whole number, then 2 and 12,765,861.5 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 25,531,723
-1 -25,531,723

Now, we try dividing 25,531,723 by 3:

25,531,723 ÷ 3 = 8,510,574.3333

If the quotient is a whole number, then 3 and 8,510,574.3333 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 25,531,723
-1 -25,531,723

Let's try dividing by 4:

25,531,723 ÷ 4 = 6,382,930.75

If the quotient is a whole number, then 4 and 6,382,930.75 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 25,531,723
-1 25,531,723
Keep dividing by the next highest number until you cannot divide anymore.

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

17432713013131,8972,19111,65313,45981,57184,82394,213593,7613,647,38925,531,723
-1-7-43-271-301-313-1,897-2,191-11,653-13,459-81,571-84,823-94,213-593,761-3,647,389-25,531,723

More Examples

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