Q: What are the factor combinations of the number 1,720,009?

 A:
Positive:   1 x 172000917 x 10117723 x 7478353 x 3245383 x 20723391 x 4399901 x 19091219 x 1411
Negative: -1 x -1720009-17 x -101177-23 x -74783-53 x -32453-83 x -20723-391 x -4399-901 x -1909-1219 x -1411


How do I find the factor combinations of the number 1,720,009?

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 1,720,009, 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 1,720,009
-1 -1,720,009

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 1,720,009.

Example:
1 x 1,720,009 = 1,720,009
and
-1 x -1,720,009 = 1,720,009
Notice both answers equal 1,720,009

With that explanation out of the way, let's continue. Next, we take the number 1,720,009 and divide it by 2:

1,720,009 ÷ 2 = 860,004.5

If the quotient is a whole number, then 2 and 860,004.5 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 1,720,009
-1 -1,720,009

Now, we try dividing 1,720,009 by 3:

1,720,009 ÷ 3 = 573,336.3333

If the quotient is a whole number, then 3 and 573,336.3333 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 1,720,009
-1 -1,720,009

Let's try dividing by 4:

1,720,009 ÷ 4 = 430,002.25

If the quotient is a whole number, then 4 and 430,002.25 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 1,720,009
-1 1,720,009
Keep dividing by the next highest number until you cannot divide anymore.

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

1172353833919011,2191,4111,9094,39920,72332,45374,783101,1771,720,009
-1-17-23-53-83-391-901-1,219-1,411-1,909-4,399-20,723-32,453-74,783-101,177-1,720,009

More Examples

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