Q: What are the factor combinations of the number 103,616,105?

 A:
Positive:   1 x 1036161055 x 2072322117 x 609506531 x 334245585 x 1219013155 x 668491527 x 1966152635 x 39323
Negative: -1 x -103616105-5 x -20723221-17 x -6095065-31 x -3342455-85 x -1219013-155 x -668491-527 x -196615-2635 x -39323


How do I find the factor combinations of the number 103,616,105?

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 103,616,105, 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.

1 103,616,105
-1 -103,616,105

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 103,616,105.

Example:
1 x 103,616,105 = 103,616,105
and
-1 x -103,616,105 = 103,616,105
Notice both answers equal 103,616,105

With that explanation out of the way, let's continue. Next, we take the number 103,616,105 and divide it by 2:

103,616,105 ÷ 2 = 51,808,052.5

If the quotient is a whole number, then 2 and 51,808,052.5 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:

1 103,616,105
-1 -103,616,105

Now, we try dividing 103,616,105 by 3:

103,616,105 ÷ 3 = 34,538,701.6667

If the quotient is a whole number, then 3 and 34,538,701.6667 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:

1 103,616,105
-1 -103,616,105

Let's try dividing by 4:

103,616,105 ÷ 4 = 25,904,026.25

If the quotient is a whole number, then 4 and 25,904,026.25 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:

1 103,616,105
-1 103,616,105
Keep dividing by the next highest number until you cannot divide anymore.

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

151731851555272,63539,323196,615668,4911,219,0133,342,4556,095,06520,723,221103,616,105
-1-5-17-31-85-155-527-2,635-39,323-196,615-668,491-1,219,013-3,342,455-6,095,065-20,723,221-103,616,105

More Examples

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