Q: What are the factor combinations of the number 386,425?

 A:
Positive:   1 x 3864255 x 7728513 x 2972525 x 1545729 x 1332541 x 942565 x 5945145 x 2665205 x 1885325 x 1189377 x 1025533 x 725
Negative: -1 x -386425-5 x -77285-13 x -29725-25 x -15457-29 x -13325-41 x -9425-65 x -5945-145 x -2665-205 x -1885-325 x -1189-377 x -1025-533 x -725


How do I find the factor combinations of the number 386,425?

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 386,425, 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.

1 386,425
-1 -386,425

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 386,425.

Example:
1 x 386,425 = 386,425
and
-1 x -386,425 = 386,425
Notice both answers equal 386,425

With that explanation out of the way, let's continue. Next, we take the number 386,425 and divide it by 2:

386,425 ÷ 2 = 193,212.5

If the quotient is a whole number, then 2 and 193,212.5 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:

1 386,425
-1 -386,425

Now, we try dividing 386,425 by 3:

386,425 ÷ 3 = 128,808.3333

If the quotient is a whole number, then 3 and 128,808.3333 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:

1 386,425
-1 -386,425

Let's try dividing by 4:

386,425 ÷ 4 = 96,606.25

If the quotient is a whole number, then 4 and 96,606.25 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:

1 386,425
-1 386,425
Keep dividing by the next highest number until you cannot divide anymore.

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

1513252941651452053253775337251,0251,1891,8852,6655,9459,42513,32515,45729,72577,285386,425
-1-5-13-25-29-41-65-145-205-325-377-533-725-1,025-1,189-1,885-2,665-5,945-9,425-13,325-15,457-29,725-77,285-386,425

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