Q: What are the factor combinations of the number 17,077,109?

 A:
Positive:   1 x 170771097 x 243958723 x 74248373 x 233933161 x 106069511 x 334191453 x 117531679 x 10171
Negative: -1 x -17077109-7 x -2439587-23 x -742483-73 x -233933-161 x -106069-511 x -33419-1453 x -11753-1679 x -10171


How do I find the factor combinations of the number 17,077,109?

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 17,077,109, 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 17,077,109
-1 -17,077,109

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 17,077,109.

Example:
1 x 17,077,109 = 17,077,109
and
-1 x -17,077,109 = 17,077,109
Notice both answers equal 17,077,109

With that explanation out of the way, let's continue. Next, we take the number 17,077,109 and divide it by 2:

17,077,109 ÷ 2 = 8,538,554.5

If the quotient is a whole number, then 2 and 8,538,554.5 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 17,077,109
-1 -17,077,109

Now, we try dividing 17,077,109 by 3:

17,077,109 ÷ 3 = 5,692,369.6667

If the quotient is a whole number, then 3 and 5,692,369.6667 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 17,077,109
-1 -17,077,109

Let's try dividing by 4:

17,077,109 ÷ 4 = 4,269,277.25

If the quotient is a whole number, then 4 and 4,269,277.25 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 17,077,109
-1 17,077,109
Keep dividing by the next highest number until you cannot divide anymore.

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

1723731615111,4531,67910,17111,75333,419106,069233,933742,4832,439,58717,077,109
-1-7-23-73-161-511-1,453-1,679-10,171-11,753-33,419-106,069-233,933-742,483-2,439,587-17,077,109

More Examples

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