Q: What are the factor combinations of the number 133,321,133?

 A:
Positive:   1 x 13332113311 x 1212010323 x 5796571253 x 526961433 x 3079011217 x 1095494763 x 279919959 x 13387
Negative: -1 x -133321133-11 x -12120103-23 x -5796571-253 x -526961-433 x -307901-1217 x -109549-4763 x -27991-9959 x -13387


How do I find the factor combinations of the number 133,321,133?

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 133,321,133, 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.

1 133,321,133
-1 -133,321,133

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 133,321,133.

Example:
1 x 133,321,133 = 133,321,133
and
-1 x -133,321,133 = 133,321,133
Notice both answers equal 133,321,133

With that explanation out of the way, let's continue. Next, we take the number 133,321,133 and divide it by 2:

133,321,133 ÷ 2 = 66,660,566.5

If the quotient is a whole number, then 2 and 66,660,566.5 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:

1 133,321,133
-1 -133,321,133

Now, we try dividing 133,321,133 by 3:

133,321,133 ÷ 3 = 44,440,377.6667

If the quotient is a whole number, then 3 and 44,440,377.6667 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:

1 133,321,133
-1 -133,321,133

Let's try dividing by 4:

133,321,133 ÷ 4 = 33,330,283.25

If the quotient is a whole number, then 4 and 33,330,283.25 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:

1 133,321,133
-1 133,321,133
Keep dividing by the next highest number until you cannot divide anymore.

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

111232534331,2174,7639,95913,38727,991109,549307,901526,9615,796,57112,120,103133,321,133
-1-11-23-253-433-1,217-4,763-9,959-13,387-27,991-109,549-307,901-526,961-5,796,571-12,120,103-133,321,133

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