Q: What are the factor combinations of the number 311,395?

 A:
Positive:   1 x 3113955 x 622797 x 4448531 x 1004535 x 889741 x 759549 x 6355155 x 2009205 x 1519217 x 1435245 x 1271287 x 1085
Negative: -1 x -311395-5 x -62279-7 x -44485-31 x -10045-35 x -8897-41 x -7595-49 x -6355-155 x -2009-205 x -1519-217 x -1435-245 x -1271-287 x -1085


How do I find the factor combinations of the number 311,395?

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 311,395, 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.

1 311,395
-1 -311,395

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 311,395.

Example:
1 x 311,395 = 311,395
and
-1 x -311,395 = 311,395
Notice both answers equal 311,395

With that explanation out of the way, let's continue. Next, we take the number 311,395 and divide it by 2:

311,395 ÷ 2 = 155,697.5

If the quotient is a whole number, then 2 and 155,697.5 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:

1 311,395
-1 -311,395

Now, we try dividing 311,395 by 3:

311,395 ÷ 3 = 103,798.3333

If the quotient is a whole number, then 3 and 103,798.3333 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:

1 311,395
-1 -311,395

Let's try dividing by 4:

311,395 ÷ 4 = 77,848.75

If the quotient is a whole number, then 4 and 77,848.75 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:

1 311,395
-1 311,395
Keep dividing by the next highest number until you cannot divide anymore.

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

157313541491552052172452871,0851,2711,4351,5192,0096,3557,5958,89710,04544,48562,279311,395
-1-5-7-31-35-41-49-155-205-217-245-287-1,085-1,271-1,435-1,519-2,009-6,355-7,595-8,897-10,045-44,485-62,279-311,395

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