Q: What are the factor combinations of the number 214,324,135?

 A:
Positive:   1 x 2143241355 x 42864827751 x 2853853755 x 57077
Negative: -1 x -214324135-5 x -42864827-751 x -285385-3755 x -57077


How do I find the factor combinations of the number 214,324,135?

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 214,324,135, 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.

1 214,324,135
-1 -214,324,135

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 214,324,135.

Example:
1 x 214,324,135 = 214,324,135
and
-1 x -214,324,135 = 214,324,135
Notice both answers equal 214,324,135

With that explanation out of the way, let's continue. Next, we take the number 214,324,135 and divide it by 2:

214,324,135 ÷ 2 = 107,162,067.5

If the quotient is a whole number, then 2 and 107,162,067.5 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:

1 214,324,135
-1 -214,324,135

Now, we try dividing 214,324,135 by 3:

214,324,135 ÷ 3 = 71,441,378.3333

If the quotient is a whole number, then 3 and 71,441,378.3333 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:

1 214,324,135
-1 -214,324,135

Let's try dividing by 4:

214,324,135 ÷ 4 = 53,581,033.75

If the quotient is a whole number, then 4 and 53,581,033.75 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:

1 214,324,135
-1 214,324,135
Keep dividing by the next highest number until you cannot divide anymore.

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

157513,75557,077285,38542,864,827214,324,135
-1-5-751-3,755-57,077-285,385-42,864,827-214,324,135

More Examples

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