Q: What are the factor combinations of the number 1,010,305?

 A:
Positive:   1 x 10103055 x 202061
Negative: -1 x -1010305-5 x -202061


How do I find the factor combinations of the number 1,010,305?

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 1,010,305, 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 1,010,305
-1 -1,010,305

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 1,010,305.

Example:
1 x 1,010,305 = 1,010,305
and
-1 x -1,010,305 = 1,010,305
Notice both answers equal 1,010,305

With that explanation out of the way, let's continue. Next, we take the number 1,010,305 and divide it by 2:

1,010,305 ÷ 2 = 505,152.5

If the quotient is a whole number, then 2 and 505,152.5 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 1,010,305
-1 -1,010,305

Now, we try dividing 1,010,305 by 3:

1,010,305 ÷ 3 = 336,768.3333

If the quotient is a whole number, then 3 and 336,768.3333 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 1,010,305
-1 -1,010,305

Let's try dividing by 4:

1,010,305 ÷ 4 = 252,576.25

If the quotient is a whole number, then 4 and 252,576.25 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 1,010,305
-1 1,010,305
Keep dividing by the next highest number until you cannot divide anymore.

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

15202,0611,010,305
-1-5-202,061-1,010,305

More Examples

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