Q: What are the factor combinations of the number 104,350,609?

 A:
Positive:   1 x 10435060911 x 948641923 x 4536983253 x 412453277 x 3767171489 x 700813047 x 342476371 x 16379
Negative: -1 x -104350609-11 x -9486419-23 x -4536983-253 x -412453-277 x -376717-1489 x -70081-3047 x -34247-6371 x -16379


How do I find the factor combinations of the number 104,350,609?

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 104,350,609, 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.

1 104,350,609
-1 -104,350,609

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 104,350,609.

Example:
1 x 104,350,609 = 104,350,609
and
-1 x -104,350,609 = 104,350,609
Notice both answers equal 104,350,609

With that explanation out of the way, let's continue. Next, we take the number 104,350,609 and divide it by 2:

104,350,609 ÷ 2 = 52,175,304.5

If the quotient is a whole number, then 2 and 52,175,304.5 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:

1 104,350,609
-1 -104,350,609

Now, we try dividing 104,350,609 by 3:

104,350,609 ÷ 3 = 34,783,536.3333

If the quotient is a whole number, then 3 and 34,783,536.3333 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:

1 104,350,609
-1 -104,350,609

Let's try dividing by 4:

104,350,609 ÷ 4 = 26,087,652.25

If the quotient is a whole number, then 4 and 26,087,652.25 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:

1 104,350,609
-1 104,350,609
Keep dividing by the next highest number until you cannot divide anymore.

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

111232532771,4893,0476,37116,37934,24770,081376,717412,4534,536,9839,486,419104,350,609
-1-11-23-253-277-1,489-3,047-6,371-16,379-34,247-70,081-376,717-412,453-4,536,983-9,486,419-104,350,609

More Examples

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