Q: What are the factor combinations of the number 505,037?

 A:
Positive:   1 x 50503713 x 3884953 x 9529689 x 733
Negative: -1 x -505037-13 x -38849-53 x -9529-689 x -733


How do I find the factor combinations of the number 505,037?

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 505,037, 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.

1 505,037
-1 -505,037

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 505,037.

Example:
1 x 505,037 = 505,037
and
-1 x -505,037 = 505,037
Notice both answers equal 505,037

With that explanation out of the way, let's continue. Next, we take the number 505,037 and divide it by 2:

505,037 ÷ 2 = 252,518.5

If the quotient is a whole number, then 2 and 252,518.5 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:

1 505,037
-1 -505,037

Now, we try dividing 505,037 by 3:

505,037 ÷ 3 = 168,345.6667

If the quotient is a whole number, then 3 and 168,345.6667 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:

1 505,037
-1 -505,037

Let's try dividing by 4:

505,037 ÷ 4 = 126,259.25

If the quotient is a whole number, then 4 and 126,259.25 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:

1 505,037
-1 505,037
Keep dividing by the next highest number until you cannot divide anymore.

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

113536897339,52938,849505,037
-1-13-53-689-733-9,529-38,849-505,037

More Examples

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