Q: What are the factor combinations of the number 100,805,735?

 A:
Positive:   1 x 1008057355 x 2016114719 x 530556553 x 190199595 x 1061113265 x 3803991007 x 1001055035 x 20021
Negative: -1 x -100805735-5 x -20161147-19 x -5305565-53 x -1901995-95 x -1061113-265 x -380399-1007 x -100105-5035 x -20021


How do I find the factor combinations of the number 100,805,735?

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 100,805,735, 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.

1 100,805,735
-1 -100,805,735

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 100,805,735.

Example:
1 x 100,805,735 = 100,805,735
and
-1 x -100,805,735 = 100,805,735
Notice both answers equal 100,805,735

With that explanation out of the way, let's continue. Next, we take the number 100,805,735 and divide it by 2:

100,805,735 ÷ 2 = 50,402,867.5

If the quotient is a whole number, then 2 and 50,402,867.5 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:

1 100,805,735
-1 -100,805,735

Now, we try dividing 100,805,735 by 3:

100,805,735 ÷ 3 = 33,601,911.6667

If the quotient is a whole number, then 3 and 33,601,911.6667 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:

1 100,805,735
-1 -100,805,735

Let's try dividing by 4:

100,805,735 ÷ 4 = 25,201,433.75

If the quotient is a whole number, then 4 and 25,201,433.75 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:

1 100,805,735
-1 100,805,735
Keep dividing by the next highest number until you cannot divide anymore.

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

151953952651,0075,03520,021100,105380,3991,061,1131,901,9955,305,56520,161,147100,805,735
-1-5-19-53-95-265-1,007-5,035-20,021-100,105-380,399-1,061,113-1,901,995-5,305,565-20,161,147-100,805,735

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