Q: What are the factor combinations of the number 12,467,021?

 A:
Positive:   1 x 124670217 x 178100319 x 65615949 x 254429133 x 93737343 x 36347931 x 133911913 x 6517
Negative: -1 x -12467021-7 x -1781003-19 x -656159-49 x -254429-133 x -93737-343 x -36347-931 x -13391-1913 x -6517


How do I find the factor combinations of the number 12,467,021?

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 12,467,021, 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 12,467,021
-1 -12,467,021

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 12,467,021.

Example:
1 x 12,467,021 = 12,467,021
and
-1 x -12,467,021 = 12,467,021
Notice both answers equal 12,467,021

With that explanation out of the way, let's continue. Next, we take the number 12,467,021 and divide it by 2:

12,467,021 ÷ 2 = 6,233,510.5

If the quotient is a whole number, then 2 and 6,233,510.5 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 12,467,021
-1 -12,467,021

Now, we try dividing 12,467,021 by 3:

12,467,021 ÷ 3 = 4,155,673.6667

If the quotient is a whole number, then 3 and 4,155,673.6667 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 12,467,021
-1 -12,467,021

Let's try dividing by 4:

12,467,021 ÷ 4 = 3,116,755.25

If the quotient is a whole number, then 4 and 3,116,755.25 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 12,467,021
-1 12,467,021
Keep dividing by the next highest number until you cannot divide anymore.

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

1719491333439311,9136,51713,39136,34793,737254,429656,1591,781,00312,467,021
-1-7-19-49-133-343-931-1,913-6,517-13,391-36,347-93,737-254,429-656,159-1,781,003-12,467,021

More Examples

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