Q: What are the factor combinations of the number 360,398,105?

 A:
Positive:   1 x 3603981055 x 72079621223 x 1616135263 x 13703351115 x 3232271229 x 2932451315 x 2740676145 x 58649
Negative: -1 x -360398105-5 x -72079621-223 x -1616135-263 x -1370335-1115 x -323227-1229 x -293245-1315 x -274067-6145 x -58649


How do I find the factor combinations of the number 360,398,105?

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 360,398,105, 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.

1 360,398,105
-1 -360,398,105

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 360,398,105.

Example:
1 x 360,398,105 = 360,398,105
and
-1 x -360,398,105 = 360,398,105
Notice both answers equal 360,398,105

With that explanation out of the way, let's continue. Next, we take the number 360,398,105 and divide it by 2:

360,398,105 ÷ 2 = 180,199,052.5

If the quotient is a whole number, then 2 and 180,199,052.5 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:

1 360,398,105
-1 -360,398,105

Now, we try dividing 360,398,105 by 3:

360,398,105 ÷ 3 = 120,132,701.6667

If the quotient is a whole number, then 3 and 120,132,701.6667 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:

1 360,398,105
-1 -360,398,105

Let's try dividing by 4:

360,398,105 ÷ 4 = 90,099,526.25

If the quotient is a whole number, then 4 and 90,099,526.25 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:

1 360,398,105
-1 360,398,105
Keep dividing by the next highest number until you cannot divide anymore.

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

152232631,1151,2291,3156,14558,649274,067293,245323,2271,370,3351,616,13572,079,621360,398,105
-1-5-223-263-1,115-1,229-1,315-6,145-58,649-274,067-293,245-323,227-1,370,335-1,616,135-72,079,621-360,398,105

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