Q: What are the factor combinations of the number 23,689,105?

 A:
Positive:   1 x 236891055 x 473782111 x 215355519 x 124679555 x 43071195 x 249359209 x 1133451045 x 22669
Negative: -1 x -23689105-5 x -4737821-11 x -2153555-19 x -1246795-55 x -430711-95 x -249359-209 x -113345-1045 x -22669


How do I find the factor combinations of the number 23,689,105?

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 23,689,105, 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 23,689,105
-1 -23,689,105

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 23,689,105.

Example:
1 x 23,689,105 = 23,689,105
and
-1 x -23,689,105 = 23,689,105
Notice both answers equal 23,689,105

With that explanation out of the way, let's continue. Next, we take the number 23,689,105 and divide it by 2:

23,689,105 ÷ 2 = 11,844,552.5

If the quotient is a whole number, then 2 and 11,844,552.5 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 23,689,105
-1 -23,689,105

Now, we try dividing 23,689,105 by 3:

23,689,105 ÷ 3 = 7,896,368.3333

If the quotient is a whole number, then 3 and 7,896,368.3333 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 23,689,105
-1 -23,689,105

Let's try dividing by 4:

23,689,105 ÷ 4 = 5,922,276.25

If the quotient is a whole number, then 4 and 5,922,276.25 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 23,689,105
-1 23,689,105
Keep dividing by the next highest number until you cannot divide anymore.

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

15111955952091,04522,669113,345249,359430,7111,246,7952,153,5554,737,82123,689,105
-1-5-11-19-55-95-209-1,045-22,669-113,345-249,359-430,711-1,246,795-2,153,555-4,737,821-23,689,105

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