Q: What are the factor combinations of the number 23,000,215?

 A:
Positive:   1 x 230002155 x 46000437 x 328574535 x 657149257 x 894951285 x 178991799 x 127852557 x 8995
Negative: -1 x -23000215-5 x -4600043-7 x -3285745-35 x -657149-257 x -89495-1285 x -17899-1799 x -12785-2557 x -8995


How do I find the factor combinations of the number 23,000,215?

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 23,000,215, 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 23,000,215
-1 -23,000,215

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 23,000,215.

Example:
1 x 23,000,215 = 23,000,215
and
-1 x -23,000,215 = 23,000,215
Notice both answers equal 23,000,215

With that explanation out of the way, let's continue. Next, we take the number 23,000,215 and divide it by 2:

23,000,215 ÷ 2 = 11,500,107.5

If the quotient is a whole number, then 2 and 11,500,107.5 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 23,000,215
-1 -23,000,215

Now, we try dividing 23,000,215 by 3:

23,000,215 ÷ 3 = 7,666,738.3333

If the quotient is a whole number, then 3 and 7,666,738.3333 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 23,000,215
-1 -23,000,215

Let's try dividing by 4:

23,000,215 ÷ 4 = 5,750,053.75

If the quotient is a whole number, then 4 and 5,750,053.75 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 23,000,215
-1 23,000,215
Keep dividing by the next highest number until you cannot divide anymore.

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

157352571,2851,7992,5578,99512,78517,89989,495657,1493,285,7454,600,04323,000,215
-1-5-7-35-257-1,285-1,799-2,557-8,995-12,785-17,899-89,495-657,149-3,285,745-4,600,043-23,000,215

More Examples

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