Q: What are the factor combinations of the number 100,407,673?

 A:
Positive:   1 x 10040767323 x 436555183 x 1209731149 x 673877353 x 2844411909 x 525973427 x 292998119 x 12367
Negative: -1 x -100407673-23 x -4365551-83 x -1209731-149 x -673877-353 x -284441-1909 x -52597-3427 x -29299-8119 x -12367


How do I find the factor combinations of the number 100,407,673?

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 100,407,673, 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.

1 100,407,673
-1 -100,407,673

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 100,407,673.

Example:
1 x 100,407,673 = 100,407,673
and
-1 x -100,407,673 = 100,407,673
Notice both answers equal 100,407,673

With that explanation out of the way, let's continue. Next, we take the number 100,407,673 and divide it by 2:

100,407,673 ÷ 2 = 50,203,836.5

If the quotient is a whole number, then 2 and 50,203,836.5 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:

1 100,407,673
-1 -100,407,673

Now, we try dividing 100,407,673 by 3:

100,407,673 ÷ 3 = 33,469,224.3333

If the quotient is a whole number, then 3 and 33,469,224.3333 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:

1 100,407,673
-1 -100,407,673

Let's try dividing by 4:

100,407,673 ÷ 4 = 25,101,918.25

If the quotient is a whole number, then 4 and 25,101,918.25 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:

1 100,407,673
-1 100,407,673
Keep dividing by the next highest number until you cannot divide anymore.

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

123831493531,9093,4278,11912,36729,29952,597284,441673,8771,209,7314,365,551100,407,673
-1-23-83-149-353-1,909-3,427-8,119-12,367-29,299-52,597-284,441-673,877-1,209,731-4,365,551-100,407,673

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