Q: What are the factor combinations of the number 17,217,431?

 A:
Positive:   1 x 172174317 x 245963311 x 156522131 x 55540177 x 223603217 x 79343341 x 504912387 x 7213
Negative: -1 x -17217431-7 x -2459633-11 x -1565221-31 x -555401-77 x -223603-217 x -79343-341 x -50491-2387 x -7213


How do I find the factor combinations of the number 17,217,431?

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 17,217,431, 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 17,217,431
-1 -17,217,431

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 17,217,431.

Example:
1 x 17,217,431 = 17,217,431
and
-1 x -17,217,431 = 17,217,431
Notice both answers equal 17,217,431

With that explanation out of the way, let's continue. Next, we take the number 17,217,431 and divide it by 2:

17,217,431 ÷ 2 = 8,608,715.5

If the quotient is a whole number, then 2 and 8,608,715.5 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 17,217,431
-1 -17,217,431

Now, we try dividing 17,217,431 by 3:

17,217,431 ÷ 3 = 5,739,143.6667

If the quotient is a whole number, then 3 and 5,739,143.6667 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 17,217,431
-1 -17,217,431

Let's try dividing by 4:

17,217,431 ÷ 4 = 4,304,357.75

If the quotient is a whole number, then 4 and 4,304,357.75 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 17,217,431
-1 17,217,431
Keep dividing by the next highest number until you cannot divide anymore.

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

171131772173412,3877,21350,49179,343223,603555,4011,565,2212,459,63317,217,431
-1-7-11-31-77-217-341-2,387-7,213-50,491-79,343-223,603-555,401-1,565,221-2,459,633-17,217,431

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