Q: What are the factor combinations of the number 11,000,309?

 A:
Positive:   1 x 1100030917 x 64707729 x 37932153 x 207553421 x 26129493 x 22313901 x 122091537 x 7157
Negative: -1 x -11000309-17 x -647077-29 x -379321-53 x -207553-421 x -26129-493 x -22313-901 x -12209-1537 x -7157


How do I find the factor combinations of the number 11,000,309?

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 11,000,309, 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 11,000,309
-1 -11,000,309

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 11,000,309.

Example:
1 x 11,000,309 = 11,000,309
and
-1 x -11,000,309 = 11,000,309
Notice both answers equal 11,000,309

With that explanation out of the way, let's continue. Next, we take the number 11,000,309 and divide it by 2:

11,000,309 ÷ 2 = 5,500,154.5

If the quotient is a whole number, then 2 and 5,500,154.5 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 11,000,309
-1 -11,000,309

Now, we try dividing 11,000,309 by 3:

11,000,309 ÷ 3 = 3,666,769.6667

If the quotient is a whole number, then 3 and 3,666,769.6667 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 11,000,309
-1 -11,000,309

Let's try dividing by 4:

11,000,309 ÷ 4 = 2,750,077.25

If the quotient is a whole number, then 4 and 2,750,077.25 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 11,000,309
-1 11,000,309
Keep dividing by the next highest number until you cannot divide anymore.

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

11729534214939011,5377,15712,20922,31326,129207,553379,321647,07711,000,309
-1-17-29-53-421-493-901-1,537-7,157-12,209-22,313-26,129-207,553-379,321-647,077-11,000,309

More Examples

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