Q: What are the factor combinations of the number 413,140,308?

 A:
Positive:   1 x 4131403082 x 2065701543 x 1377134364 x 1032850776 x 688567187 x 5902004412 x 3442835914 x 2951002221 x 1967334828 x 1475501142 x 983667484 x 4918337
Negative: -1 x -413140308-2 x -206570154-3 x -137713436-4 x -103285077-6 x -68856718-7 x -59020044-12 x -34428359-14 x -29510022-21 x -19673348-28 x -14755011-42 x -9836674-84 x -4918337


How do I find the factor combinations of the number 413,140,308?

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 413,140,308, 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.

1 413,140,308
-1 -413,140,308

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 413,140,308.

Example:
1 x 413,140,308 = 413,140,308
and
-1 x -413,140,308 = 413,140,308
Notice both answers equal 413,140,308

With that explanation out of the way, let's continue. Next, we take the number 413,140,308 and divide it by 2:

413,140,308 ÷ 2 = 206,570,154

If the quotient is a whole number, then 2 and 206,570,154 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 206,570,154 413,140,308
-1 -2 -206,570,154 -413,140,308

Now, we try dividing 413,140,308 by 3:

413,140,308 ÷ 3 = 137,713,436

If the quotient is a whole number, then 3 and 137,713,436 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 137,713,436 206,570,154 413,140,308
-1 -2 -3 -137,713,436 -206,570,154 -413,140,308

Let's try dividing by 4:

413,140,308 ÷ 4 = 103,285,077

If the quotient is a whole number, then 4 and 103,285,077 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 103,285,077 137,713,436 206,570,154 413,140,308
-1 -2 -3 -4 -103,285,077 -137,713,436 -206,570,154 413,140,308
Keep dividing by the next highest number until you cannot divide anymore.

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

1234671214212842844,918,3379,836,67414,755,01119,673,34829,510,02234,428,35959,020,04468,856,718103,285,077137,713,436206,570,154413,140,308
-1-2-3-4-6-7-12-14-21-28-42-84-4,918,337-9,836,674-14,755,011-19,673,348-29,510,022-34,428,359-59,020,044-68,856,718-103,285,077-137,713,436-206,570,154-413,140,308

More Examples

Here are some more numbers to try:

413,140,306413,140,307413,140,309413,140,310
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