Q: What are the factor combinations of the number 3,509,231?

 A:
Positive:   1 x 350923111 x 31902131 x 11320141 x 85591251 x 13981341 x 10291451 x 77811271 x 2761
Negative: -1 x -3509231-11 x -319021-31 x -113201-41 x -85591-251 x -13981-341 x -10291-451 x -7781-1271 x -2761


How do I find the factor combinations of the number 3,509,231?

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 3,509,231, 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 3,509,231
-1 -3,509,231

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 3,509,231.

Example:
1 x 3,509,231 = 3,509,231
and
-1 x -3,509,231 = 3,509,231
Notice both answers equal 3,509,231

With that explanation out of the way, let's continue. Next, we take the number 3,509,231 and divide it by 2:

3,509,231 ÷ 2 = 1,754,615.5

If the quotient is a whole number, then 2 and 1,754,615.5 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 3,509,231
-1 -3,509,231

Now, we try dividing 3,509,231 by 3:

3,509,231 ÷ 3 = 1,169,743.6667

If the quotient is a whole number, then 3 and 1,169,743.6667 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 3,509,231
-1 -3,509,231

Let's try dividing by 4:

3,509,231 ÷ 4 = 877,307.75

If the quotient is a whole number, then 4 and 877,307.75 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 3,509,231
-1 3,509,231
Keep dividing by the next highest number until you cannot divide anymore.

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

11131412513414511,2712,7617,78110,29113,98185,591113,201319,0213,509,231
-1-11-31-41-251-341-451-1,271-2,761-7,781-10,291-13,981-85,591-113,201-319,021-3,509,231

More Examples

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