Q: What are the factor combinations of the number 1,500,605?

 A:
Positive:   1 x 15006055 x 30012129 x 5174579 x 18995131 x 11455145 x 10349395 x 3799655 x 2291
Negative: -1 x -1500605-5 x -300121-29 x -51745-79 x -18995-131 x -11455-145 x -10349-395 x -3799-655 x -2291


How do I find the factor combinations of the number 1,500,605?

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 1,500,605, 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 1,500,605
-1 -1,500,605

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 1,500,605.

Example:
1 x 1,500,605 = 1,500,605
and
-1 x -1,500,605 = 1,500,605
Notice both answers equal 1,500,605

With that explanation out of the way, let's continue. Next, we take the number 1,500,605 and divide it by 2:

1,500,605 ÷ 2 = 750,302.5

If the quotient is a whole number, then 2 and 750,302.5 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 1,500,605
-1 -1,500,605

Now, we try dividing 1,500,605 by 3:

1,500,605 ÷ 3 = 500,201.6667

If the quotient is a whole number, then 3 and 500,201.6667 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 1,500,605
-1 -1,500,605

Let's try dividing by 4:

1,500,605 ÷ 4 = 375,151.25

If the quotient is a whole number, then 4 and 375,151.25 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 1,500,605
-1 1,500,605
Keep dividing by the next highest number until you cannot divide anymore.

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

1529791311453956552,2913,79910,34911,45518,99551,745300,1211,500,605
-1-5-29-79-131-145-395-655-2,291-3,799-10,349-11,455-18,995-51,745-300,121-1,500,605

More Examples

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