Q: What are the factor combinations of the number 109,102,777?

 A:
Positive:   1 x 1091027777 x 1558611123 x 4743599161 x 677657
Negative: -1 x -109102777-7 x -15586111-23 x -4743599-161 x -677657


How do I find the factor combinations of the number 109,102,777?

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 109,102,777, 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.

1 109,102,777
-1 -109,102,777

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 109,102,777.

Example:
1 x 109,102,777 = 109,102,777
and
-1 x -109,102,777 = 109,102,777
Notice both answers equal 109,102,777

With that explanation out of the way, let's continue. Next, we take the number 109,102,777 and divide it by 2:

109,102,777 ÷ 2 = 54,551,388.5

If the quotient is a whole number, then 2 and 54,551,388.5 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:

1 109,102,777
-1 -109,102,777

Now, we try dividing 109,102,777 by 3:

109,102,777 ÷ 3 = 36,367,592.3333

If the quotient is a whole number, then 3 and 36,367,592.3333 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:

1 109,102,777
-1 -109,102,777

Let's try dividing by 4:

109,102,777 ÷ 4 = 27,275,694.25

If the quotient is a whole number, then 4 and 27,275,694.25 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:

1 109,102,777
-1 109,102,777
Keep dividing by the next highest number until you cannot divide anymore.

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

1723161677,6574,743,59915,586,111109,102,777
-1-7-23-161-677,657-4,743,599-15,586,111-109,102,777

More Examples

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