Q: What are the factor combinations of the number 1,297,009?

 A:
Positive:   1 x 12970097 x 18528731 x 4183943 x 30163139 x 9331217 x 5977301 x 4309973 x 1333
Negative: -1 x -1297009-7 x -185287-31 x -41839-43 x -30163-139 x -9331-217 x -5977-301 x -4309-973 x -1333


How do I find the factor combinations of the number 1,297,009?

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 1,297,009, 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 1,297,009
-1 -1,297,009

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 1,297,009.

Example:
1 x 1,297,009 = 1,297,009
and
-1 x -1,297,009 = 1,297,009
Notice both answers equal 1,297,009

With that explanation out of the way, let's continue. Next, we take the number 1,297,009 and divide it by 2:

1,297,009 ÷ 2 = 648,504.5

If the quotient is a whole number, then 2 and 648,504.5 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 1,297,009
-1 -1,297,009

Now, we try dividing 1,297,009 by 3:

1,297,009 ÷ 3 = 432,336.3333

If the quotient is a whole number, then 3 and 432,336.3333 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 1,297,009
-1 -1,297,009

Let's try dividing by 4:

1,297,009 ÷ 4 = 324,252.25

If the quotient is a whole number, then 4 and 324,252.25 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 1,297,009
-1 1,297,009
Keep dividing by the next highest number until you cannot divide anymore.

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

1731431392173019731,3334,3095,9779,33130,16341,839185,2871,297,009
-1-7-31-43-139-217-301-973-1,333-4,309-5,977-9,331-30,163-41,839-185,287-1,297,009

More Examples

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