Q: What are the factor combinations of the number 200,311,321?

 A:
Positive:   1 x 2003113217 x 2861590347 x 426194389 x 2250689329 x 608849623 x 3215274183 x 478876841 x 29281
Negative: -1 x -200311321-7 x -28615903-47 x -4261943-89 x -2250689-329 x -608849-623 x -321527-4183 x -47887-6841 x -29281


How do I find the factor combinations of the number 200,311,321?

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 200,311,321, 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.

1 200,311,321
-1 -200,311,321

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 200,311,321.

Example:
1 x 200,311,321 = 200,311,321
and
-1 x -200,311,321 = 200,311,321
Notice both answers equal 200,311,321

With that explanation out of the way, let's continue. Next, we take the number 200,311,321 and divide it by 2:

200,311,321 ÷ 2 = 100,155,660.5

If the quotient is a whole number, then 2 and 100,155,660.5 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:

1 200,311,321
-1 -200,311,321

Now, we try dividing 200,311,321 by 3:

200,311,321 ÷ 3 = 66,770,440.3333

If the quotient is a whole number, then 3 and 66,770,440.3333 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:

1 200,311,321
-1 -200,311,321

Let's try dividing by 4:

200,311,321 ÷ 4 = 50,077,830.25

If the quotient is a whole number, then 4 and 50,077,830.25 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:

1 200,311,321
-1 200,311,321
Keep dividing by the next highest number until you cannot divide anymore.

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

1747893296234,1836,84129,28147,887321,527608,8492,250,6894,261,94328,615,903200,311,321
-1-7-47-89-329-623-4,183-6,841-29,281-47,887-321,527-608,849-2,250,689-4,261,943-28,615,903-200,311,321

More Examples

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