Q: What are the factor combinations of the number 45,216,017?

 A:
Positive:   1 x 452160177 x 645943111 x 411054729 x 155917377 x 587221203 x 222739319 x 1417432233 x 20249
Negative: -1 x -45216017-7 x -6459431-11 x -4110547-29 x -1559173-77 x -587221-203 x -222739-319 x -141743-2233 x -20249


How do I find the factor combinations of the number 45,216,017?

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 45,216,017, 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 45,216,017
-1 -45,216,017

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 45,216,017.

Example:
1 x 45,216,017 = 45,216,017
and
-1 x -45,216,017 = 45,216,017
Notice both answers equal 45,216,017

With that explanation out of the way, let's continue. Next, we take the number 45,216,017 and divide it by 2:

45,216,017 ÷ 2 = 22,608,008.5

If the quotient is a whole number, then 2 and 22,608,008.5 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 45,216,017
-1 -45,216,017

Now, we try dividing 45,216,017 by 3:

45,216,017 ÷ 3 = 15,072,005.6667

If the quotient is a whole number, then 3 and 15,072,005.6667 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 45,216,017
-1 -45,216,017

Let's try dividing by 4:

45,216,017 ÷ 4 = 11,304,004.25

If the quotient is a whole number, then 4 and 11,304,004.25 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 45,216,017
-1 45,216,017
Keep dividing by the next highest number until you cannot divide anymore.

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

171129772033192,23320,249141,743222,739587,2211,559,1734,110,5476,459,43145,216,017
-1-7-11-29-77-203-319-2,233-20,249-141,743-222,739-587,221-1,559,173-4,110,547-6,459,431-45,216,017

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