Q: What are the factor combinations of the number 222,396?

 A:
Positive:   1 x 2223962 x 1111983 x 741324 x 555996 x 3706612 x 1853343 x 517286 x 2586129 x 1724172 x 1293258 x 862431 x 516
Negative: -1 x -222396-2 x -111198-3 x -74132-4 x -55599-6 x -37066-12 x -18533-43 x -5172-86 x -2586-129 x -1724-172 x -1293-258 x -862-431 x -516


How do I find the factor combinations of the number 222,396?

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 222,396, 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.

1 222,396
-1 -222,396

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 222,396.

Example:
1 x 222,396 = 222,396
and
-1 x -222,396 = 222,396
Notice both answers equal 222,396

With that explanation out of the way, let's continue. Next, we take the number 222,396 and divide it by 2:

222,396 ÷ 2 = 111,198

If the quotient is a whole number, then 2 and 111,198 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 111,198 222,396
-1 -2 -111,198 -222,396

Now, we try dividing 222,396 by 3:

222,396 ÷ 3 = 74,132

If the quotient is a whole number, then 3 and 74,132 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 74,132 111,198 222,396
-1 -2 -3 -74,132 -111,198 -222,396

Let's try dividing by 4:

222,396 ÷ 4 = 55,599

If the quotient is a whole number, then 4 and 55,599 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 55,599 74,132 111,198 222,396
-1 -2 -3 -4 -55,599 -74,132 -111,198 222,396
Keep dividing by the next highest number until you cannot divide anymore.

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

123461243861291722584315168621,2931,7242,5865,17218,53337,06655,59974,132111,198222,396
-1-2-3-4-6-12-43-86-129-172-258-431-516-862-1,293-1,724-2,586-5,172-18,533-37,066-55,599-74,132-111,198-222,396

More Examples

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