Q: What are the factor combinations of the number 1,010,009?

 A:
Positive:   1 x 10100097 x 14428711 x 9181913 x 7769377 x 1311791 x 11099143 x 70631001 x 1009
Negative: -1 x -1010009-7 x -144287-11 x -91819-13 x -77693-77 x -13117-91 x -11099-143 x -7063-1001 x -1009


How do I find the factor combinations of the number 1,010,009?

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 1,010,009, 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 1,010,009
-1 -1,010,009

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 1,010,009.

Example:
1 x 1,010,009 = 1,010,009
and
-1 x -1,010,009 = 1,010,009
Notice both answers equal 1,010,009

With that explanation out of the way, let's continue. Next, we take the number 1,010,009 and divide it by 2:

1,010,009 ÷ 2 = 505,004.5

If the quotient is a whole number, then 2 and 505,004.5 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 1,010,009
-1 -1,010,009

Now, we try dividing 1,010,009 by 3:

1,010,009 ÷ 3 = 336,669.6667

If the quotient is a whole number, then 3 and 336,669.6667 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 1,010,009
-1 -1,010,009

Let's try dividing by 4:

1,010,009 ÷ 4 = 252,502.25

If the quotient is a whole number, then 4 and 252,502.25 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 1,010,009
-1 1,010,009
Keep dividing by the next highest number until you cannot divide anymore.

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

17111377911431,0011,0097,06311,09913,11777,69391,819144,2871,010,009
-1-7-11-13-77-91-143-1,001-1,009-7,063-11,099-13,117-77,693-91,819-144,287-1,010,009

More Examples

Here are some more numbers to try:

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