Q: What are the factor combinations of the number 424,332,209?

 A:
Positive:   1 x 4243322097 x 6061888749 x 8659841101 x 4201309179 x 2370571479 x 885871707 x 6001871253 x 3386533353 x 1265534949 x 857418771 x 4837918079 x 23471
Negative: -1 x -424332209-7 x -60618887-49 x -8659841-101 x -4201309-179 x -2370571-479 x -885871-707 x -600187-1253 x -338653-3353 x -126553-4949 x -85741-8771 x -48379-18079 x -23471


How do I find the factor combinations of the number 424,332,209?

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 424,332,209, 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.

1 424,332,209
-1 -424,332,209

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 424,332,209.

Example:
1 x 424,332,209 = 424,332,209
and
-1 x -424,332,209 = 424,332,209
Notice both answers equal 424,332,209

With that explanation out of the way, let's continue. Next, we take the number 424,332,209 and divide it by 2:

424,332,209 ÷ 2 = 212,166,104.5

If the quotient is a whole number, then 2 and 212,166,104.5 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:

1 424,332,209
-1 -424,332,209

Now, we try dividing 424,332,209 by 3:

424,332,209 ÷ 3 = 141,444,069.6667

If the quotient is a whole number, then 3 and 141,444,069.6667 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:

1 424,332,209
-1 -424,332,209

Let's try dividing by 4:

424,332,209 ÷ 4 = 106,083,052.25

If the quotient is a whole number, then 4 and 106,083,052.25 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:

1 424,332,209
-1 424,332,209
Keep dividing by the next highest number until you cannot divide anymore.

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

17491011794797071,2533,3534,9498,77118,07923,47148,37985,741126,553338,653600,187885,8712,370,5714,201,3098,659,84160,618,887424,332,209
-1-7-49-101-179-479-707-1,253-3,353-4,949-8,771-18,079-23,471-48,379-85,741-126,553-338,653-600,187-885,871-2,370,571-4,201,309-8,659,841-60,618,887-424,332,209

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