Q: What are the factor combinations of the number 311,514,445?

 A:
Positive:   1 x 3115144455 x 6230288911 x 2831949555 x 5663899113 x 2756765565 x 5513531243 x 2506156215 x 50123
Negative: -1 x -311514445-5 x -62302889-11 x -28319495-55 x -5663899-113 x -2756765-565 x -551353-1243 x -250615-6215 x -50123


How do I find the factor combinations of the number 311,514,445?

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 311,514,445, 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.

1 311,514,445
-1 -311,514,445

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 311,514,445.

Example:
1 x 311,514,445 = 311,514,445
and
-1 x -311,514,445 = 311,514,445
Notice both answers equal 311,514,445

With that explanation out of the way, let's continue. Next, we take the number 311,514,445 and divide it by 2:

311,514,445 ÷ 2 = 155,757,222.5

If the quotient is a whole number, then 2 and 155,757,222.5 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:

1 311,514,445
-1 -311,514,445

Now, we try dividing 311,514,445 by 3:

311,514,445 ÷ 3 = 103,838,148.3333

If the quotient is a whole number, then 3 and 103,838,148.3333 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:

1 311,514,445
-1 -311,514,445

Let's try dividing by 4:

311,514,445 ÷ 4 = 77,878,611.25

If the quotient is a whole number, then 4 and 77,878,611.25 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:

1 311,514,445
-1 311,514,445
Keep dividing by the next highest number until you cannot divide anymore.

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

1511551135651,2436,21550,123250,615551,3532,756,7655,663,89928,319,49562,302,889311,514,445
-1-5-11-55-113-565-1,243-6,215-50,123-250,615-551,353-2,756,765-5,663,899-28,319,495-62,302,889-311,514,445

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