Q: What are the factor combinations of the number 384,307?

 A:
Positive:   1 x 3843077 x 5490111 x 3493723 x 1670931 x 1239749 x 784377 x 4991161 x 2387217 x 1771253 x 1519341 x 1127539 x 713
Negative: -1 x -384307-7 x -54901-11 x -34937-23 x -16709-31 x -12397-49 x -7843-77 x -4991-161 x -2387-217 x -1771-253 x -1519-341 x -1127-539 x -713


How do I find the factor combinations of the number 384,307?

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 384,307, 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.

1 384,307
-1 -384,307

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 384,307.

Example:
1 x 384,307 = 384,307
and
-1 x -384,307 = 384,307
Notice both answers equal 384,307

With that explanation out of the way, let's continue. Next, we take the number 384,307 and divide it by 2:

384,307 ÷ 2 = 192,153.5

If the quotient is a whole number, then 2 and 192,153.5 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:

1 384,307
-1 -384,307

Now, we try dividing 384,307 by 3:

384,307 ÷ 3 = 128,102.3333

If the quotient is a whole number, then 3 and 128,102.3333 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:

1 384,307
-1 -384,307

Let's try dividing by 4:

384,307 ÷ 4 = 96,076.75

If the quotient is a whole number, then 4 and 96,076.75 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:

1 384,307
-1 384,307
Keep dividing by the next highest number until you cannot divide anymore.

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

1711233149771612172533415397131,1271,5191,7712,3874,9917,84312,39716,70934,93754,901384,307
-1-7-11-23-31-49-77-161-217-253-341-539-713-1,127-1,519-1,771-2,387-4,991-7,843-12,397-16,709-34,937-54,901-384,307

More Examples

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