Q: What are the factor combinations of the number 1,230,121?

 A:
Positive:   1 x 1230121661 x 1861
Negative: -1 x -1230121-661 x -1861


How do I find the factor combinations of the number 1,230,121?

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 1,230,121, 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 1,230,121
-1 -1,230,121

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 1,230,121.

Example:
1 x 1,230,121 = 1,230,121
and
-1 x -1,230,121 = 1,230,121
Notice both answers equal 1,230,121

With that explanation out of the way, let's continue. Next, we take the number 1,230,121 and divide it by 2:

1,230,121 ÷ 2 = 615,060.5

If the quotient is a whole number, then 2 and 615,060.5 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 1,230,121
-1 -1,230,121

Now, we try dividing 1,230,121 by 3:

1,230,121 ÷ 3 = 410,040.3333

If the quotient is a whole number, then 3 and 410,040.3333 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 1,230,121
-1 -1,230,121

Let's try dividing by 4:

1,230,121 ÷ 4 = 307,530.25

If the quotient is a whole number, then 4 and 307,530.25 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 1,230,121
-1 1,230,121
Keep dividing by the next highest number until you cannot divide anymore.

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

16611,8611,230,121
-1-661-1,861-1,230,121

More Examples

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