Q: What are the factor combinations of the number 14,134,121?

 A:
Positive:   1 x 1413412123 x 614527
Negative: -1 x -14134121-23 x -614527


How do I find the factor combinations of the number 14,134,121?

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 14,134,121, 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 14,134,121
-1 -14,134,121

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 14,134,121.

Example:
1 x 14,134,121 = 14,134,121
and
-1 x -14,134,121 = 14,134,121
Notice both answers equal 14,134,121

With that explanation out of the way, let's continue. Next, we take the number 14,134,121 and divide it by 2:

14,134,121 ÷ 2 = 7,067,060.5

If the quotient is a whole number, then 2 and 7,067,060.5 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 14,134,121
-1 -14,134,121

Now, we try dividing 14,134,121 by 3:

14,134,121 ÷ 3 = 4,711,373.6667

If the quotient is a whole number, then 3 and 4,711,373.6667 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 14,134,121
-1 -14,134,121

Let's try dividing by 4:

14,134,121 ÷ 4 = 3,533,530.25

If the quotient is a whole number, then 4 and 3,533,530.25 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 14,134,121
-1 14,134,121
Keep dividing by the next highest number until you cannot divide anymore.

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

123614,52714,134,121
-1-23-614,527-14,134,121

More Examples

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