Q: What are the factor combinations of the number 22,120,189?

 A:
Positive:   1 x 221201897 x 316002713 x 170155343 x 51442391 x 243079301 x 73489559 x 395713913 x 5653
Negative: -1 x -22120189-7 x -3160027-13 x -1701553-43 x -514423-91 x -243079-301 x -73489-559 x -39571-3913 x -5653


How do I find the factor combinations of the number 22,120,189?

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 22,120,189, 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 22,120,189
-1 -22,120,189

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 22,120,189.

Example:
1 x 22,120,189 = 22,120,189
and
-1 x -22,120,189 = 22,120,189
Notice both answers equal 22,120,189

With that explanation out of the way, let's continue. Next, we take the number 22,120,189 and divide it by 2:

22,120,189 ÷ 2 = 11,060,094.5

If the quotient is a whole number, then 2 and 11,060,094.5 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 22,120,189
-1 -22,120,189

Now, we try dividing 22,120,189 by 3:

22,120,189 ÷ 3 = 7,373,396.3333

If the quotient is a whole number, then 3 and 7,373,396.3333 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 22,120,189
-1 -22,120,189

Let's try dividing by 4:

22,120,189 ÷ 4 = 5,530,047.25

If the quotient is a whole number, then 4 and 5,530,047.25 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 22,120,189
-1 22,120,189
Keep dividing by the next highest number until you cannot divide anymore.

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

171343913015593,9135,65339,57173,489243,079514,4231,701,5533,160,02722,120,189
-1-7-13-43-91-301-559-3,913-5,653-39,571-73,489-243,079-514,423-1,701,553-3,160,027-22,120,189

More Examples

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