Q: What are the factor combinations of the number 121,203,421?

 A:
Positive:   1 x 12120342117 x 712961341 x 295618153 x 2286857193 x 627997289 x 419389697 x 173893901 x 1345212173 x 557773281 x 369417913 x 1531710229 x 11849
Negative: -1 x -121203421-17 x -7129613-41 x -2956181-53 x -2286857-193 x -627997-289 x -419389-697 x -173893-901 x -134521-2173 x -55777-3281 x -36941-7913 x -15317-10229 x -11849


How do I find the factor combinations of the number 121,203,421?

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 121,203,421, 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.

1 121,203,421
-1 -121,203,421

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 121,203,421.

Example:
1 x 121,203,421 = 121,203,421
and
-1 x -121,203,421 = 121,203,421
Notice both answers equal 121,203,421

With that explanation out of the way, let's continue. Next, we take the number 121,203,421 and divide it by 2:

121,203,421 ÷ 2 = 60,601,710.5

If the quotient is a whole number, then 2 and 60,601,710.5 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:

1 121,203,421
-1 -121,203,421

Now, we try dividing 121,203,421 by 3:

121,203,421 ÷ 3 = 40,401,140.3333

If the quotient is a whole number, then 3 and 40,401,140.3333 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:

1 121,203,421
-1 -121,203,421

Let's try dividing by 4:

121,203,421 ÷ 4 = 30,300,855.25

If the quotient is a whole number, then 4 and 30,300,855.25 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:

1 121,203,421
-1 121,203,421
Keep dividing by the next highest number until you cannot divide anymore.

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

11741531932896979012,1733,2817,91310,22911,84915,31736,94155,777134,521173,893419,389627,9972,286,8572,956,1817,129,613121,203,421
-1-17-41-53-193-289-697-901-2,173-3,281-7,913-10,229-11,849-15,317-36,941-55,777-134,521-173,893-419,389-627,997-2,286,857-2,956,181-7,129,613-121,203,421

More Examples

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