Q: What are the factor combinations of the number 72,356,021?

 A:
Positive:   1 x 7235602141 x 176478179 x 91589989 x 812989251 x 2882713239 x 223393649 x 198297031 x 10291
Negative: -1 x -72356021-41 x -1764781-79 x -915899-89 x -812989-251 x -288271-3239 x -22339-3649 x -19829-7031 x -10291


How do I find the factor combinations of the number 72,356,021?

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 72,356,021, 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 72,356,021
-1 -72,356,021

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 72,356,021.

Example:
1 x 72,356,021 = 72,356,021
and
-1 x -72,356,021 = 72,356,021
Notice both answers equal 72,356,021

With that explanation out of the way, let's continue. Next, we take the number 72,356,021 and divide it by 2:

72,356,021 ÷ 2 = 36,178,010.5

If the quotient is a whole number, then 2 and 36,178,010.5 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 72,356,021
-1 -72,356,021

Now, we try dividing 72,356,021 by 3:

72,356,021 ÷ 3 = 24,118,673.6667

If the quotient is a whole number, then 3 and 24,118,673.6667 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 72,356,021
-1 -72,356,021

Let's try dividing by 4:

72,356,021 ÷ 4 = 18,089,005.25

If the quotient is a whole number, then 4 and 18,089,005.25 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 72,356,021
-1 72,356,021
Keep dividing by the next highest number until you cannot divide anymore.

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

14179892513,2393,6497,03110,29119,82922,339288,271812,989915,8991,764,78172,356,021
-1-41-79-89-251-3,239-3,649-7,031-10,291-19,829-22,339-288,271-812,989-915,899-1,764,781-72,356,021

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