Q: What are the factor combinations of the number 134,404,309?

 A:
Positive:   1 x 13440430913 x 1033879319 x 7073911247 x 544147263 x 5110432069 x 649613419 x 393114997 x 26897
Negative: -1 x -134404309-13 x -10338793-19 x -7073911-247 x -544147-263 x -511043-2069 x -64961-3419 x -39311-4997 x -26897


How do I find the factor combinations of the number 134,404,309?

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 134,404,309, 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.

1 134,404,309
-1 -134,404,309

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 134,404,309.

Example:
1 x 134,404,309 = 134,404,309
and
-1 x -134,404,309 = 134,404,309
Notice both answers equal 134,404,309

With that explanation out of the way, let's continue. Next, we take the number 134,404,309 and divide it by 2:

134,404,309 ÷ 2 = 67,202,154.5

If the quotient is a whole number, then 2 and 67,202,154.5 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:

1 134,404,309
-1 -134,404,309

Now, we try dividing 134,404,309 by 3:

134,404,309 ÷ 3 = 44,801,436.3333

If the quotient is a whole number, then 3 and 44,801,436.3333 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:

1 134,404,309
-1 -134,404,309

Let's try dividing by 4:

134,404,309 ÷ 4 = 33,601,077.25

If the quotient is a whole number, then 4 and 33,601,077.25 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:

1 134,404,309
-1 134,404,309
Keep dividing by the next highest number until you cannot divide anymore.

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

113192472632,0693,4194,99726,89739,31164,961511,043544,1477,073,91110,338,793134,404,309
-1-13-19-247-263-2,069-3,419-4,997-26,897-39,311-64,961-511,043-544,147-7,073,911-10,338,793-134,404,309

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