Q: What are the factor combinations of the number 105,103,427?

 A:
Positive:   1 x 10510342711 x 955485713 x 808487961 x 1723007143 x 734989671 x 156637793 x 1325398723 x 12049
Negative: -1 x -105103427-11 x -9554857-13 x -8084879-61 x -1723007-143 x -734989-671 x -156637-793 x -132539-8723 x -12049


How do I find the factor combinations of the number 105,103,427?

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 105,103,427, 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.

1 105,103,427
-1 -105,103,427

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 105,103,427.

Example:
1 x 105,103,427 = 105,103,427
and
-1 x -105,103,427 = 105,103,427
Notice both answers equal 105,103,427

With that explanation out of the way, let's continue. Next, we take the number 105,103,427 and divide it by 2:

105,103,427 ÷ 2 = 52,551,713.5

If the quotient is a whole number, then 2 and 52,551,713.5 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:

1 105,103,427
-1 -105,103,427

Now, we try dividing 105,103,427 by 3:

105,103,427 ÷ 3 = 35,034,475.6667

If the quotient is a whole number, then 3 and 35,034,475.6667 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:

1 105,103,427
-1 -105,103,427

Let's try dividing by 4:

105,103,427 ÷ 4 = 26,275,856.75

If the quotient is a whole number, then 4 and 26,275,856.75 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:

1 105,103,427
-1 105,103,427
Keep dividing by the next highest number until you cannot divide anymore.

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

11113611436717938,72312,049132,539156,637734,9891,723,0078,084,8799,554,857105,103,427
-1-11-13-61-143-671-793-8,723-12,049-132,539-156,637-734,989-1,723,007-8,084,879-9,554,857-105,103,427

More Examples

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