Q: What are the factor combinations of the number 14,120,315?

 A:
Positive:   1 x 141203155 x 282406311 x 128366555 x 256733139 x 101585695 x 203171529 x 92351847 x 7645
Negative: -1 x -14120315-5 x -2824063-11 x -1283665-55 x -256733-139 x -101585-695 x -20317-1529 x -9235-1847 x -7645


How do I find the factor combinations of the number 14,120,315?

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 14,120,315, 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 14,120,315
-1 -14,120,315

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 14,120,315.

Example:
1 x 14,120,315 = 14,120,315
and
-1 x -14,120,315 = 14,120,315
Notice both answers equal 14,120,315

With that explanation out of the way, let's continue. Next, we take the number 14,120,315 and divide it by 2:

14,120,315 ÷ 2 = 7,060,157.5

If the quotient is a whole number, then 2 and 7,060,157.5 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 14,120,315
-1 -14,120,315

Now, we try dividing 14,120,315 by 3:

14,120,315 ÷ 3 = 4,706,771.6667

If the quotient is a whole number, then 3 and 4,706,771.6667 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 14,120,315
-1 -14,120,315

Let's try dividing by 4:

14,120,315 ÷ 4 = 3,530,078.75

If the quotient is a whole number, then 4 and 3,530,078.75 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 14,120,315
-1 14,120,315
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551396951,5291,8477,6459,23520,317101,585256,7331,283,6652,824,06314,120,315
-1-5-11-55-139-695-1,529-1,847-7,645-9,235-20,317-101,585-256,733-1,283,665-2,824,063-14,120,315

More Examples

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