Q: What are the factor combinations of the number 9,725,365?

 A:
Positive:   1 x 97253655 x 194507313 x 74810565 x 149621157 x 61945785 x 12389953 x 102052041 x 4765
Negative: -1 x -9725365-5 x -1945073-13 x -748105-65 x -149621-157 x -61945-785 x -12389-953 x -10205-2041 x -4765


How do I find the factor combinations of the number 9,725,365?

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 9,725,365, 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 9,725,365
-1 -9,725,365

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 9,725,365.

Example:
1 x 9,725,365 = 9,725,365
and
-1 x -9,725,365 = 9,725,365
Notice both answers equal 9,725,365

With that explanation out of the way, let's continue. Next, we take the number 9,725,365 and divide it by 2:

9,725,365 ÷ 2 = 4,862,682.5

If the quotient is a whole number, then 2 and 4,862,682.5 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 9,725,365
-1 -9,725,365

Now, we try dividing 9,725,365 by 3:

9,725,365 ÷ 3 = 3,241,788.3333

If the quotient is a whole number, then 3 and 3,241,788.3333 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 9,725,365
-1 -9,725,365

Let's try dividing by 4:

9,725,365 ÷ 4 = 2,431,341.25

If the quotient is a whole number, then 4 and 2,431,341.25 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 9,725,365
-1 9,725,365
Keep dividing by the next highest number until you cannot divide anymore.

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

1513651577859532,0414,76510,20512,38961,945149,621748,1051,945,0739,725,365
-1-5-13-65-157-785-953-2,041-4,765-10,205-12,389-61,945-149,621-748,105-1,945,073-9,725,365

More Examples

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