Q: What are the factor combinations of the number 23,652,137?

 A:
Positive:   1 x 23652137
Negative: -1 x -23652137


How do I find the factor combinations of the number 23,652,137?

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 23,652,137, 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 23,652,137
-1 -23,652,137

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 23,652,137.

Example:
1 x 23,652,137 = 23,652,137
and
-1 x -23,652,137 = 23,652,137
Notice both answers equal 23,652,137

With that explanation out of the way, let's continue. Next, we take the number 23,652,137 and divide it by 2:

23,652,137 ÷ 2 = 11,826,068.5

If the quotient is a whole number, then 2 and 11,826,068.5 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 23,652,137
-1 -23,652,137

Now, we try dividing 23,652,137 by 3:

23,652,137 ÷ 3 = 7,884,045.6667

If the quotient is a whole number, then 3 and 7,884,045.6667 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 23,652,137
-1 -23,652,137

Let's try dividing by 4:

23,652,137 ÷ 4 = 5,913,034.25

If the quotient is a whole number, then 4 and 5,913,034.25 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 23,652,137
-1 23,652,137
Keep dividing by the next highest number until you cannot divide anymore.

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

123,652,137
-1-23,652,137

More Examples

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