Q: What are the factor combinations of the number 120,553,261?

 A:
Positive:   1 x 12055326129 x 415700947 x 2564963241 x 500221367 x 3284831363 x 884476989 x 1724910643 x 11327
Negative: -1 x -120553261-29 x -4157009-47 x -2564963-241 x -500221-367 x -328483-1363 x -88447-6989 x -17249-10643 x -11327


How do I find the factor combinations of the number 120,553,261?

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 120,553,261, 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.

1 120,553,261
-1 -120,553,261

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 120,553,261.

Example:
1 x 120,553,261 = 120,553,261
and
-1 x -120,553,261 = 120,553,261
Notice both answers equal 120,553,261

With that explanation out of the way, let's continue. Next, we take the number 120,553,261 and divide it by 2:

120,553,261 ÷ 2 = 60,276,630.5

If the quotient is a whole number, then 2 and 60,276,630.5 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:

1 120,553,261
-1 -120,553,261

Now, we try dividing 120,553,261 by 3:

120,553,261 ÷ 3 = 40,184,420.3333

If the quotient is a whole number, then 3 and 40,184,420.3333 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:

1 120,553,261
-1 -120,553,261

Let's try dividing by 4:

120,553,261 ÷ 4 = 30,138,315.25

If the quotient is a whole number, then 4 and 30,138,315.25 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:

1 120,553,261
-1 120,553,261
Keep dividing by the next highest number until you cannot divide anymore.

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

129472413671,3636,98910,64311,32717,24988,447328,483500,2212,564,9634,157,009120,553,261
-1-29-47-241-367-1,363-6,989-10,643-11,327-17,249-88,447-328,483-500,221-2,564,963-4,157,009-120,553,261

More Examples

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