Q: What are the factor combinations of the number 12,421,235?

 A:
Positive:   1 x 124212355 x 248424731 x 400685127 x 97805155 x 80137631 x 19685635 x 195613155 x 3937
Negative: -1 x -12421235-5 x -2484247-31 x -400685-127 x -97805-155 x -80137-631 x -19685-635 x -19561-3155 x -3937


How do I find the factor combinations of the number 12,421,235?

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 12,421,235, 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 12,421,235
-1 -12,421,235

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 12,421,235.

Example:
1 x 12,421,235 = 12,421,235
and
-1 x -12,421,235 = 12,421,235
Notice both answers equal 12,421,235

With that explanation out of the way, let's continue. Next, we take the number 12,421,235 and divide it by 2:

12,421,235 ÷ 2 = 6,210,617.5

If the quotient is a whole number, then 2 and 6,210,617.5 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 12,421,235
-1 -12,421,235

Now, we try dividing 12,421,235 by 3:

12,421,235 ÷ 3 = 4,140,411.6667

If the quotient is a whole number, then 3 and 4,140,411.6667 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 12,421,235
-1 -12,421,235

Let's try dividing by 4:

12,421,235 ÷ 4 = 3,105,308.75

If the quotient is a whole number, then 4 and 3,105,308.75 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 12,421,235
-1 12,421,235
Keep dividing by the next highest number until you cannot divide anymore.

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

15311271556316353,1553,93719,56119,68580,13797,805400,6852,484,24712,421,235
-1-5-31-127-155-631-635-3,155-3,937-19,561-19,685-80,137-97,805-400,685-2,484,247-12,421,235

More Examples

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