Q: What are the factor combinations of the number 75,135,542?

 A:
Positive:   1 x 751355422 x 3756777167 x 112142673 x 1029254134 x 560713146 x 5146274891 x 153627681 x 9782
Negative: -1 x -75135542-2 x -37567771-67 x -1121426-73 x -1029254-134 x -560713-146 x -514627-4891 x -15362-7681 x -9782


How do I find the factor combinations of the number 75,135,542?

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 75,135,542, 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 75,135,542
-1 -75,135,542

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 75,135,542.

Example:
1 x 75,135,542 = 75,135,542
and
-1 x -75,135,542 = 75,135,542
Notice both answers equal 75,135,542

With that explanation out of the way, let's continue. Next, we take the number 75,135,542 and divide it by 2:

75,135,542 ÷ 2 = 37,567,771

If the quotient is a whole number, then 2 and 37,567,771 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 37,567,771 75,135,542
-1 -2 -37,567,771 -75,135,542

Now, we try dividing 75,135,542 by 3:

75,135,542 ÷ 3 = 25,045,180.6667

If the quotient is a whole number, then 3 and 25,045,180.6667 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 2 37,567,771 75,135,542
-1 -2 -37,567,771 -75,135,542

Let's try dividing by 4:

75,135,542 ÷ 4 = 18,783,885.5

If the quotient is a whole number, then 4 and 18,783,885.5 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 2 37,567,771 75,135,542
-1 -2 -37,567,771 75,135,542
Keep dividing by the next highest number until you cannot divide anymore.

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

1267731341464,8917,6819,78215,362514,627560,7131,029,2541,121,42637,567,77175,135,542
-1-2-67-73-134-146-4,891-7,681-9,782-15,362-514,627-560,713-1,029,254-1,121,426-37,567,771-75,135,542

More Examples

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