Q: What are the factor combinations of the number 222,312,025?

 A:
Positive:   1 x 2223120255 x 4446240513 x 1710092525 x 889248165 x 3420185325 x 684037
Negative: -1 x -222312025-5 x -44462405-13 x -17100925-25 x -8892481-65 x -3420185-325 x -684037


How do I find the factor combinations of the number 222,312,025?

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 222,312,025, 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.

1 222,312,025
-1 -222,312,025

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 222,312,025.

Example:
1 x 222,312,025 = 222,312,025
and
-1 x -222,312,025 = 222,312,025
Notice both answers equal 222,312,025

With that explanation out of the way, let's continue. Next, we take the number 222,312,025 and divide it by 2:

222,312,025 ÷ 2 = 111,156,012.5

If the quotient is a whole number, then 2 and 111,156,012.5 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:

1 222,312,025
-1 -222,312,025

Now, we try dividing 222,312,025 by 3:

222,312,025 ÷ 3 = 74,104,008.3333

If the quotient is a whole number, then 3 and 74,104,008.3333 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:

1 222,312,025
-1 -222,312,025

Let's try dividing by 4:

222,312,025 ÷ 4 = 55,578,006.25

If the quotient is a whole number, then 4 and 55,578,006.25 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:

1 222,312,025
-1 222,312,025
Keep dividing by the next highest number until you cannot divide anymore.

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

15132565325684,0373,420,1858,892,48117,100,92544,462,405222,312,025
-1-5-13-25-65-325-684,037-3,420,185-8,892,481-17,100,925-44,462,405-222,312,025

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