Q: What are the factor combinations of the number 360,435,005?

 A:
Positive:   1 x 3604350055 x 720870017 x 5149071535 x 10298143311 x 11589551555 x 2317912177 x 16556510885 x 33113
Negative: -1 x -360435005-5 x -72087001-7 x -51490715-35 x -10298143-311 x -1158955-1555 x -231791-2177 x -165565-10885 x -33113


How do I find the factor combinations of the number 360,435,005?

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 360,435,005, 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.

1 360,435,005
-1 -360,435,005

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 360,435,005.

Example:
1 x 360,435,005 = 360,435,005
and
-1 x -360,435,005 = 360,435,005
Notice both answers equal 360,435,005

With that explanation out of the way, let's continue. Next, we take the number 360,435,005 and divide it by 2:

360,435,005 ÷ 2 = 180,217,502.5

If the quotient is a whole number, then 2 and 180,217,502.5 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:

1 360,435,005
-1 -360,435,005

Now, we try dividing 360,435,005 by 3:

360,435,005 ÷ 3 = 120,145,001.6667

If the quotient is a whole number, then 3 and 120,145,001.6667 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:

1 360,435,005
-1 -360,435,005

Let's try dividing by 4:

360,435,005 ÷ 4 = 90,108,751.25

If the quotient is a whole number, then 4 and 90,108,751.25 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:

1 360,435,005
-1 360,435,005
Keep dividing by the next highest number until you cannot divide anymore.

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

157353111,5552,17710,88533,113165,565231,7911,158,95510,298,14351,490,71572,087,001360,435,005
-1-5-7-35-311-1,555-2,177-10,885-33,113-165,565-231,791-1,158,955-10,298,143-51,490,715-72,087,001-360,435,005

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