Q: What are the factor combinations of the number 109,135,621?

 A:
Positive:   1 x 1091356217 x 1559080323 x 474502783 x 1314887161 x 677861581 x 1878411909 x 571698167 x 13363
Negative: -1 x -109135621-7 x -15590803-23 x -4745027-83 x -1314887-161 x -677861-581 x -187841-1909 x -57169-8167 x -13363


How do I find the factor combinations of the number 109,135,621?

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 109,135,621, 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.

1 109,135,621
-1 -109,135,621

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 109,135,621.

Example:
1 x 109,135,621 = 109,135,621
and
-1 x -109,135,621 = 109,135,621
Notice both answers equal 109,135,621

With that explanation out of the way, let's continue. Next, we take the number 109,135,621 and divide it by 2:

109,135,621 ÷ 2 = 54,567,810.5

If the quotient is a whole number, then 2 and 54,567,810.5 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:

1 109,135,621
-1 -109,135,621

Now, we try dividing 109,135,621 by 3:

109,135,621 ÷ 3 = 36,378,540.3333

If the quotient is a whole number, then 3 and 36,378,540.3333 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:

1 109,135,621
-1 -109,135,621

Let's try dividing by 4:

109,135,621 ÷ 4 = 27,283,905.25

If the quotient is a whole number, then 4 and 27,283,905.25 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:

1 109,135,621
-1 109,135,621
Keep dividing by the next highest number until you cannot divide anymore.

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

1723831615811,9098,16713,36357,169187,841677,8611,314,8874,745,02715,590,803109,135,621
-1-7-23-83-161-581-1,909-8,167-13,363-57,169-187,841-677,861-1,314,887-4,745,027-15,590,803-109,135,621

More Examples

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