Q: What are the factor combinations of the number 220,213,019?

 A:
Positive:   1 x 22021301913 x 1693946317 x 1295370743 x 5121233221 x 996439559 x 393941731 x 3012499503 x 23173
Negative: -1 x -220213019-13 x -16939463-17 x -12953707-43 x -5121233-221 x -996439-559 x -393941-731 x -301249-9503 x -23173


How do I find the factor combinations of the number 220,213,019?

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 220,213,019, 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.

1 220,213,019
-1 -220,213,019

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 220,213,019.

Example:
1 x 220,213,019 = 220,213,019
and
-1 x -220,213,019 = 220,213,019
Notice both answers equal 220,213,019

With that explanation out of the way, let's continue. Next, we take the number 220,213,019 and divide it by 2:

220,213,019 ÷ 2 = 110,106,509.5

If the quotient is a whole number, then 2 and 110,106,509.5 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:

1 220,213,019
-1 -220,213,019

Now, we try dividing 220,213,019 by 3:

220,213,019 ÷ 3 = 73,404,339.6667

If the quotient is a whole number, then 3 and 73,404,339.6667 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:

1 220,213,019
-1 -220,213,019

Let's try dividing by 4:

220,213,019 ÷ 4 = 55,053,254.75

If the quotient is a whole number, then 4 and 55,053,254.75 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:

1 220,213,019
-1 220,213,019
Keep dividing by the next highest number until you cannot divide anymore.

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

11317432215597319,50323,173301,249393,941996,4395,121,23312,953,70716,939,463220,213,019
-1-13-17-43-221-559-731-9,503-23,173-301,249-393,941-996,439-5,121,233-12,953,707-16,939,463-220,213,019

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