Q: What are the factor combinations of the number 109,135,645?

 A:
Positive:   1 x 1091356455 x 2182712941 x 266184547 x 2322035205 x 532369235 x 464407241 x 4528451205 x 905691927 x 566352209 x 494059635 x 113279881 x 11045
Negative: -1 x -109135645-5 x -21827129-41 x -2661845-47 x -2322035-205 x -532369-235 x -464407-241 x -452845-1205 x -90569-1927 x -56635-2209 x -49405-9635 x -11327-9881 x -11045


How do I find the factor combinations of the number 109,135,645?

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 109,135,645, 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.

1 109,135,645
-1 -109,135,645

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 109,135,645.

Example:
1 x 109,135,645 = 109,135,645
and
-1 x -109,135,645 = 109,135,645
Notice both answers equal 109,135,645

With that explanation out of the way, let's continue. Next, we take the number 109,135,645 and divide it by 2:

109,135,645 ÷ 2 = 54,567,822.5

If the quotient is a whole number, then 2 and 54,567,822.5 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:

1 109,135,645
-1 -109,135,645

Now, we try dividing 109,135,645 by 3:

109,135,645 ÷ 3 = 36,378,548.3333

If the quotient is a whole number, then 3 and 36,378,548.3333 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:

1 109,135,645
-1 -109,135,645

Let's try dividing by 4:

109,135,645 ÷ 4 = 27,283,911.25

If the quotient is a whole number, then 4 and 27,283,911.25 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:

1 109,135,645
-1 109,135,645
Keep dividing by the next highest number until you cannot divide anymore.

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

1541472052352411,2051,9272,2099,6359,88111,04511,32749,40556,63590,569452,845464,407532,3692,322,0352,661,84521,827,129109,135,645
-1-5-41-47-205-235-241-1,205-1,927-2,209-9,635-9,881-11,045-11,327-49,405-56,635-90,569-452,845-464,407-532,369-2,322,035-2,661,845-21,827,129-109,135,645

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