Q: What are the factor combinations of the number 313,300,021?

 A:
Positive:   1 x 31330002117 x 1842941329 x 1080344943 x 7286047493 x 635497731 x 4285911247 x 25124314779 x 21199
Negative: -1 x -313300021-17 x -18429413-29 x -10803449-43 x -7286047-493 x -635497-731 x -428591-1247 x -251243-14779 x -21199


How do I find the factor combinations of the number 313,300,021?

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 313,300,021, 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.

1 313,300,021
-1 -313,300,021

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 313,300,021.

Example:
1 x 313,300,021 = 313,300,021
and
-1 x -313,300,021 = 313,300,021
Notice both answers equal 313,300,021

With that explanation out of the way, let's continue. Next, we take the number 313,300,021 and divide it by 2:

313,300,021 ÷ 2 = 156,650,010.5

If the quotient is a whole number, then 2 and 156,650,010.5 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:

1 313,300,021
-1 -313,300,021

Now, we try dividing 313,300,021 by 3:

313,300,021 ÷ 3 = 104,433,340.3333

If the quotient is a whole number, then 3 and 104,433,340.3333 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:

1 313,300,021
-1 -313,300,021

Let's try dividing by 4:

313,300,021 ÷ 4 = 78,325,005.25

If the quotient is a whole number, then 4 and 78,325,005.25 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:

1 313,300,021
-1 313,300,021
Keep dividing by the next highest number until you cannot divide anymore.

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

11729434937311,24714,77921,199251,243428,591635,4977,286,04710,803,44918,429,413313,300,021
-1-17-29-43-493-731-1,247-14,779-21,199-251,243-428,591-635,497-7,286,047-10,803,449-18,429,413-313,300,021

More Examples

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