Q: What are the factor combinations of the number 220,121,293?

 A:
Positive:   1 x 2201212937 x 3144589923 x 9570491161 x 1367213223 x 9870911561 x 1410135129 x 429176131 x 35903
Negative: -1 x -220121293-7 x -31445899-23 x -9570491-161 x -1367213-223 x -987091-1561 x -141013-5129 x -42917-6131 x -35903


How do I find the factor combinations of the number 220,121,293?

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 220,121,293, 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.

1 220,121,293
-1 -220,121,293

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 220,121,293.

Example:
1 x 220,121,293 = 220,121,293
and
-1 x -220,121,293 = 220,121,293
Notice both answers equal 220,121,293

With that explanation out of the way, let's continue. Next, we take the number 220,121,293 and divide it by 2:

220,121,293 ÷ 2 = 110,060,646.5

If the quotient is a whole number, then 2 and 110,060,646.5 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:

1 220,121,293
-1 -220,121,293

Now, we try dividing 220,121,293 by 3:

220,121,293 ÷ 3 = 73,373,764.3333

If the quotient is a whole number, then 3 and 73,373,764.3333 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:

1 220,121,293
-1 -220,121,293

Let's try dividing by 4:

220,121,293 ÷ 4 = 55,030,323.25

If the quotient is a whole number, then 4 and 55,030,323.25 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:

1 220,121,293
-1 220,121,293
Keep dividing by the next highest number until you cannot divide anymore.

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

17231612231,5615,1296,13135,90342,917141,013987,0911,367,2139,570,49131,445,899220,121,293
-1-7-23-161-223-1,561-5,129-6,131-35,903-42,917-141,013-987,091-1,367,213-9,570,491-31,445,899-220,121,293

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