Q: What are the factor combinations of the number 398,905?

 A:
Positive:   1 x 3989055 x 7978113 x 3068517 x 2346519 x 2099565 x 613785 x 469395 x 4199221 x 1805247 x 1615323 x 1235361 x 1105
Negative: -1 x -398905-5 x -79781-13 x -30685-17 x -23465-19 x -20995-65 x -6137-85 x -4693-95 x -4199-221 x -1805-247 x -1615-323 x -1235-361 x -1105


How do I find the factor combinations of the number 398,905?

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 398,905, 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.

1 398,905
-1 -398,905

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 398,905.

Example:
1 x 398,905 = 398,905
and
-1 x -398,905 = 398,905
Notice both answers equal 398,905

With that explanation out of the way, let's continue. Next, we take the number 398,905 and divide it by 2:

398,905 ÷ 2 = 199,452.5

If the quotient is a whole number, then 2 and 199,452.5 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:

1 398,905
-1 -398,905

Now, we try dividing 398,905 by 3:

398,905 ÷ 3 = 132,968.3333

If the quotient is a whole number, then 3 and 132,968.3333 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:

1 398,905
-1 -398,905

Let's try dividing by 4:

398,905 ÷ 4 = 99,726.25

If the quotient is a whole number, then 4 and 99,726.25 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:

1 398,905
-1 398,905
Keep dividing by the next highest number until you cannot divide anymore.

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

151317196585952212473233611,1051,2351,6151,8054,1994,6936,13720,99523,46530,68579,781398,905
-1-5-13-17-19-65-85-95-221-247-323-361-1,105-1,235-1,615-1,805-4,199-4,693-6,137-20,995-23,465-30,685-79,781-398,905

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