Q: What are the factor combinations of the number 135,021,341?

 A:
Positive:   1 x 1350213417 x 1928876313 x 1038625791 x 1483751523 x 2581672837 x 475933661 x 368816799 x 19859
Negative: -1 x -135021341-7 x -19288763-13 x -10386257-91 x -1483751-523 x -258167-2837 x -47593-3661 x -36881-6799 x -19859


How do I find the factor combinations of the number 135,021,341?

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 135,021,341, 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.

1 135,021,341
-1 -135,021,341

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 135,021,341.

Example:
1 x 135,021,341 = 135,021,341
and
-1 x -135,021,341 = 135,021,341
Notice both answers equal 135,021,341

With that explanation out of the way, let's continue. Next, we take the number 135,021,341 and divide it by 2:

135,021,341 ÷ 2 = 67,510,670.5

If the quotient is a whole number, then 2 and 67,510,670.5 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:

1 135,021,341
-1 -135,021,341

Now, we try dividing 135,021,341 by 3:

135,021,341 ÷ 3 = 45,007,113.6667

If the quotient is a whole number, then 3 and 45,007,113.6667 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:

1 135,021,341
-1 -135,021,341

Let's try dividing by 4:

135,021,341 ÷ 4 = 33,755,335.25

If the quotient is a whole number, then 4 and 33,755,335.25 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:

1 135,021,341
-1 135,021,341
Keep dividing by the next highest number until you cannot divide anymore.

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

1713915232,8373,6616,79919,85936,88147,593258,1671,483,75110,386,25719,288,763135,021,341
-1-7-13-91-523-2,837-3,661-6,799-19,859-36,881-47,593-258,167-1,483,751-10,386,257-19,288,763-135,021,341

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