Q: What are the factor combinations of the number 154,003,109?

 A:
Positive:   1 x 15400310913 x 11846393169 x 911261191 x 806299367 x 4196272197 x 700972483 x 620234771 x 32279
Negative: -1 x -154003109-13 x -11846393-169 x -911261-191 x -806299-367 x -419627-2197 x -70097-2483 x -62023-4771 x -32279


How do I find the factor combinations of the number 154,003,109?

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 154,003,109, 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.

1 154,003,109
-1 -154,003,109

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 154,003,109.

Example:
1 x 154,003,109 = 154,003,109
and
-1 x -154,003,109 = 154,003,109
Notice both answers equal 154,003,109

With that explanation out of the way, let's continue. Next, we take the number 154,003,109 and divide it by 2:

154,003,109 ÷ 2 = 77,001,554.5

If the quotient is a whole number, then 2 and 77,001,554.5 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:

1 154,003,109
-1 -154,003,109

Now, we try dividing 154,003,109 by 3:

154,003,109 ÷ 3 = 51,334,369.6667

If the quotient is a whole number, then 3 and 51,334,369.6667 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:

1 154,003,109
-1 -154,003,109

Let's try dividing by 4:

154,003,109 ÷ 4 = 38,500,777.25

If the quotient is a whole number, then 4 and 38,500,777.25 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:

1 154,003,109
-1 154,003,109
Keep dividing by the next highest number until you cannot divide anymore.

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

1131691913672,1972,4834,77132,27962,02370,097419,627806,299911,26111,846,393154,003,109
-1-13-169-191-367-2,197-2,483-4,771-32,279-62,023-70,097-419,627-806,299-911,261-11,846,393-154,003,109

More Examples

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