Q: What are the factor combinations of the number 36,442,021?

 A:
Positive:   1 x 364420217 x 520600311 x 331291177 x 473273211 x 1727111477 x 246732243 x 162472321 x 15701
Negative: -1 x -36442021-7 x -5206003-11 x -3312911-77 x -473273-211 x -172711-1477 x -24673-2243 x -16247-2321 x -15701


How do I find the factor combinations of the number 36,442,021?

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 36,442,021, 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 36,442,021
-1 -36,442,021

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 36,442,021.

Example:
1 x 36,442,021 = 36,442,021
and
-1 x -36,442,021 = 36,442,021
Notice both answers equal 36,442,021

With that explanation out of the way, let's continue. Next, we take the number 36,442,021 and divide it by 2:

36,442,021 ÷ 2 = 18,221,010.5

If the quotient is a whole number, then 2 and 18,221,010.5 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 36,442,021
-1 -36,442,021

Now, we try dividing 36,442,021 by 3:

36,442,021 ÷ 3 = 12,147,340.3333

If the quotient is a whole number, then 3 and 12,147,340.3333 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 36,442,021
-1 -36,442,021

Let's try dividing by 4:

36,442,021 ÷ 4 = 9,110,505.25

If the quotient is a whole number, then 4 and 9,110,505.25 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 36,442,021
-1 36,442,021
Keep dividing by the next highest number until you cannot divide anymore.

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

1711772111,4772,2432,32115,70116,24724,673172,711473,2733,312,9115,206,00336,442,021
-1-7-11-77-211-1,477-2,243-2,321-15,701-16,247-24,673-172,711-473,273-3,312,911-5,206,003-36,442,021

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