Q: What are the factor combinations of the number 23,411,635?

 A:
Positive:   1 x 234116355 x 468232713 x 180089517 x 137715565 x 36017985 x 275431221 x 1059351105 x 21187
Negative: -1 x -23411635-5 x -4682327-13 x -1800895-17 x -1377155-65 x -360179-85 x -275431-221 x -105935-1105 x -21187


How do I find the factor combinations of the number 23,411,635?

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 23,411,635, 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 23,411,635
-1 -23,411,635

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 23,411,635.

Example:
1 x 23,411,635 = 23,411,635
and
-1 x -23,411,635 = 23,411,635
Notice both answers equal 23,411,635

With that explanation out of the way, let's continue. Next, we take the number 23,411,635 and divide it by 2:

23,411,635 ÷ 2 = 11,705,817.5

If the quotient is a whole number, then 2 and 11,705,817.5 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 23,411,635
-1 -23,411,635

Now, we try dividing 23,411,635 by 3:

23,411,635 ÷ 3 = 7,803,878.3333

If the quotient is a whole number, then 3 and 7,803,878.3333 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 23,411,635
-1 -23,411,635

Let's try dividing by 4:

23,411,635 ÷ 4 = 5,852,908.75

If the quotient is a whole number, then 4 and 5,852,908.75 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 23,411,635
-1 23,411,635
Keep dividing by the next highest number until you cannot divide anymore.

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

15131765852211,10521,187105,935275,431360,1791,377,1551,800,8954,682,32723,411,635
-1-5-13-17-65-85-221-1,105-21,187-105,935-275,431-360,179-1,377,155-1,800,895-4,682,327-23,411,635

More Examples

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