Q: What are the factor combinations of the number 360,412,919?

 A:
Positive:   1 x 36041291919 x 1896910141 x 8790559127 x 2837897779 x 4626612413 x 1493633643 x 989335207 x 69217
Negative: -1 x -360412919-19 x -18969101-41 x -8790559-127 x -2837897-779 x -462661-2413 x -149363-3643 x -98933-5207 x -69217


How do I find the factor combinations of the number 360,412,919?

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 360,412,919, 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.

1 360,412,919
-1 -360,412,919

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 360,412,919.

Example:
1 x 360,412,919 = 360,412,919
and
-1 x -360,412,919 = 360,412,919
Notice both answers equal 360,412,919

With that explanation out of the way, let's continue. Next, we take the number 360,412,919 and divide it by 2:

360,412,919 ÷ 2 = 180,206,459.5

If the quotient is a whole number, then 2 and 180,206,459.5 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:

1 360,412,919
-1 -360,412,919

Now, we try dividing 360,412,919 by 3:

360,412,919 ÷ 3 = 120,137,639.6667

If the quotient is a whole number, then 3 and 120,137,639.6667 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:

1 360,412,919
-1 -360,412,919

Let's try dividing by 4:

360,412,919 ÷ 4 = 90,103,229.75

If the quotient is a whole number, then 4 and 90,103,229.75 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:

1 360,412,919
-1 360,412,919
Keep dividing by the next highest number until you cannot divide anymore.

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

119411277792,4133,6435,20769,21798,933149,363462,6612,837,8978,790,55918,969,101360,412,919
-1-19-41-127-779-2,413-3,643-5,207-69,217-98,933-149,363-462,661-2,837,897-8,790,559-18,969,101-360,412,919

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 360,412,919:


Ask a Question