Q: What are the factor combinations of the number 20,146,217?

 A:
Positive:   1 x 201462177 x 287803113 x 154970991 x 221387269 x 74893823 x 244791883 x 106993497 x 5761
Negative: -1 x -20146217-7 x -2878031-13 x -1549709-91 x -221387-269 x -74893-823 x -24479-1883 x -10699-3497 x -5761


How do I find the factor combinations of the number 20,146,217?

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 20,146,217, 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 20,146,217
-1 -20,146,217

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 20,146,217.

Example:
1 x 20,146,217 = 20,146,217
and
-1 x -20,146,217 = 20,146,217
Notice both answers equal 20,146,217

With that explanation out of the way, let's continue. Next, we take the number 20,146,217 and divide it by 2:

20,146,217 ÷ 2 = 10,073,108.5

If the quotient is a whole number, then 2 and 10,073,108.5 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 20,146,217
-1 -20,146,217

Now, we try dividing 20,146,217 by 3:

20,146,217 ÷ 3 = 6,715,405.6667

If the quotient is a whole number, then 3 and 6,715,405.6667 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 20,146,217
-1 -20,146,217

Let's try dividing by 4:

20,146,217 ÷ 4 = 5,036,554.25

If the quotient is a whole number, then 4 and 5,036,554.25 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 20,146,217
-1 20,146,217
Keep dividing by the next highest number until you cannot divide anymore.

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

1713912698231,8833,4975,76110,69924,47974,893221,3871,549,7092,878,03120,146,217
-1-7-13-91-269-823-1,883-3,497-5,761-10,699-24,479-74,893-221,387-1,549,709-2,878,031-20,146,217

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