Q: What are the factor combinations of the number 103,000,105?

 A:
Positive:   1 x 1030001055 x 2060002113 x 792308565 x 158461767 x 1537315335 x 307463353 x 291785871 x 1182551765 x 583574355 x 236514489 x 229454589 x 22445
Negative: -1 x -103000105-5 x -20600021-13 x -7923085-65 x -1584617-67 x -1537315-335 x -307463-353 x -291785-871 x -118255-1765 x -58357-4355 x -23651-4489 x -22945-4589 x -22445


How do I find the factor combinations of the number 103,000,105?

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 103,000,105, 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.

1 103,000,105
-1 -103,000,105

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 103,000,105.

Example:
1 x 103,000,105 = 103,000,105
and
-1 x -103,000,105 = 103,000,105
Notice both answers equal 103,000,105

With that explanation out of the way, let's continue. Next, we take the number 103,000,105 and divide it by 2:

103,000,105 ÷ 2 = 51,500,052.5

If the quotient is a whole number, then 2 and 51,500,052.5 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:

1 103,000,105
-1 -103,000,105

Now, we try dividing 103,000,105 by 3:

103,000,105 ÷ 3 = 34,333,368.3333

If the quotient is a whole number, then 3 and 34,333,368.3333 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:

1 103,000,105
-1 -103,000,105

Let's try dividing by 4:

103,000,105 ÷ 4 = 25,750,026.25

If the quotient is a whole number, then 4 and 25,750,026.25 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:

1 103,000,105
-1 103,000,105
Keep dividing by the next highest number until you cannot divide anymore.

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

151365673353538711,7654,3554,4894,58922,44522,94523,65158,357118,255291,785307,4631,537,3151,584,6177,923,08520,600,021103,000,105
-1-5-13-65-67-335-353-871-1,765-4,355-4,489-4,589-22,445-22,945-23,651-58,357-118,255-291,785-307,463-1,537,315-1,584,617-7,923,085-20,600,021-103,000,105

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