Q: What are the factor combinations of the number 198,967,421?

 A:
Positive:   1 x 19896742161 x 326176167 x 296966389 x 2235589547 x 3637434087 x 486835429 x 366495963 x 33367
Negative: -1 x -198967421-61 x -3261761-67 x -2969663-89 x -2235589-547 x -363743-4087 x -48683-5429 x -36649-5963 x -33367


How do I find the factor combinations of the number 198,967,421?

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 198,967,421, 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.

1 198,967,421
-1 -198,967,421

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 198,967,421.

Example:
1 x 198,967,421 = 198,967,421
and
-1 x -198,967,421 = 198,967,421
Notice both answers equal 198,967,421

With that explanation out of the way, let's continue. Next, we take the number 198,967,421 and divide it by 2:

198,967,421 ÷ 2 = 99,483,710.5

If the quotient is a whole number, then 2 and 99,483,710.5 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:

1 198,967,421
-1 -198,967,421

Now, we try dividing 198,967,421 by 3:

198,967,421 ÷ 3 = 66,322,473.6667

If the quotient is a whole number, then 3 and 66,322,473.6667 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:

1 198,967,421
-1 -198,967,421

Let's try dividing by 4:

198,967,421 ÷ 4 = 49,741,855.25

If the quotient is a whole number, then 4 and 49,741,855.25 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:

1 198,967,421
-1 198,967,421
Keep dividing by the next highest number until you cannot divide anymore.

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

16167895474,0875,4295,96333,36736,64948,683363,7432,235,5892,969,6633,261,761198,967,421
-1-61-67-89-547-4,087-5,429-5,963-33,367-36,649-48,683-363,743-2,235,589-2,969,663-3,261,761-198,967,421

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