Q: What are the factor combinations of the number 408,012,385?

 A:
Positive:   1 x 4080123855 x 8160247711 x 3709203555 x 7418407157 x 2598805785 x 5197611727 x 2362558635 x 47251
Negative: -1 x -408012385-5 x -81602477-11 x -37092035-55 x -7418407-157 x -2598805-785 x -519761-1727 x -236255-8635 x -47251


How do I find the factor combinations of the number 408,012,385?

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 408,012,385, 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.

1 408,012,385
-1 -408,012,385

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 408,012,385.

Example:
1 x 408,012,385 = 408,012,385
and
-1 x -408,012,385 = 408,012,385
Notice both answers equal 408,012,385

With that explanation out of the way, let's continue. Next, we take the number 408,012,385 and divide it by 2:

408,012,385 ÷ 2 = 204,006,192.5

If the quotient is a whole number, then 2 and 204,006,192.5 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:

1 408,012,385
-1 -408,012,385

Now, we try dividing 408,012,385 by 3:

408,012,385 ÷ 3 = 136,004,128.3333

If the quotient is a whole number, then 3 and 136,004,128.3333 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:

1 408,012,385
-1 -408,012,385

Let's try dividing by 4:

408,012,385 ÷ 4 = 102,003,096.25

If the quotient is a whole number, then 4 and 102,003,096.25 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:

1 408,012,385
-1 408,012,385
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551577851,7278,63547,251236,255519,7612,598,8057,418,40737,092,03581,602,477408,012,385
-1-5-11-55-157-785-1,727-8,635-47,251-236,255-519,761-2,598,805-7,418,407-37,092,035-81,602,477-408,012,385

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