Q: What are the factor combinations of the number 5,500,105?

 A:
Positive:   1 x 55001055 x 110002113 x 42308523 x 23913565 x 84617115 x 47827169 x 32545283 x 19435299 x 18395845 x 65091415 x 38871495 x 3679
Negative: -1 x -5500105-5 x -1100021-13 x -423085-23 x -239135-65 x -84617-115 x -47827-169 x -32545-283 x -19435-299 x -18395-845 x -6509-1415 x -3887-1495 x -3679


How do I find the factor combinations of the number 5,500,105?

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 5,500,105, 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 5,500,105
-1 -5,500,105

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 5,500,105.

Example:
1 x 5,500,105 = 5,500,105
and
-1 x -5,500,105 = 5,500,105
Notice both answers equal 5,500,105

With that explanation out of the way, let's continue. Next, we take the number 5,500,105 and divide it by 2:

5,500,105 ÷ 2 = 2,750,052.5

If the quotient is a whole number, then 2 and 2,750,052.5 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 5,500,105
-1 -5,500,105

Now, we try dividing 5,500,105 by 3:

5,500,105 ÷ 3 = 1,833,368.3333

If the quotient is a whole number, then 3 and 1,833,368.3333 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 5,500,105
-1 -5,500,105

Let's try dividing by 4:

5,500,105 ÷ 4 = 1,375,026.25

If the quotient is a whole number, then 4 and 1,375,026.25 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 5,500,105
-1 5,500,105
Keep dividing by the next highest number until you cannot divide anymore.

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

151323651151692832998451,4151,4953,6793,8876,50918,39519,43532,54547,82784,617239,135423,0851,100,0215,500,105
-1-5-13-23-65-115-169-283-299-845-1,415-1,495-3,679-3,887-6,509-18,395-19,435-32,545-47,827-84,617-239,135-423,085-1,100,021-5,500,105

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