Q: What are the factor combinations of the number 23,234,035?

 A:
Positive:   1 x 232340355 x 464680711 x 211218531 x 74948555 x 422437155 x 149897341 x 681351705 x 13627
Negative: -1 x -23234035-5 x -4646807-11 x -2112185-31 x -749485-55 x -422437-155 x -149897-341 x -68135-1705 x -13627


How do I find the factor combinations of the number 23,234,035?

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 23,234,035, 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 23,234,035
-1 -23,234,035

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 23,234,035.

Example:
1 x 23,234,035 = 23,234,035
and
-1 x -23,234,035 = 23,234,035
Notice both answers equal 23,234,035

With that explanation out of the way, let's continue. Next, we take the number 23,234,035 and divide it by 2:

23,234,035 ÷ 2 = 11,617,017.5

If the quotient is a whole number, then 2 and 11,617,017.5 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 23,234,035
-1 -23,234,035

Now, we try dividing 23,234,035 by 3:

23,234,035 ÷ 3 = 7,744,678.3333

If the quotient is a whole number, then 3 and 7,744,678.3333 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 23,234,035
-1 -23,234,035

Let's try dividing by 4:

23,234,035 ÷ 4 = 5,808,508.75

If the quotient is a whole number, then 4 and 5,808,508.75 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 23,234,035
-1 23,234,035
Keep dividing by the next highest number until you cannot divide anymore.

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

151131551553411,70513,62768,135149,897422,437749,4852,112,1854,646,80723,234,035
-1-5-11-31-55-155-341-1,705-13,627-68,135-149,897-422,437-749,485-2,112,185-4,646,807-23,234,035

More Examples

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