Q: What are the factor combinations of the number 520,405,105?

 A:
Positive:   1 x 5204051055 x 10408102111 x 4730955517 x 3061206555 x 946191185 x 6122413187 x 2782915935 x 556583
Negative: -1 x -520405105-5 x -104081021-11 x -47309555-17 x -30612065-55 x -9461911-85 x -6122413-187 x -2782915-935 x -556583


How do I find the factor combinations of the number 520,405,105?

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 520,405,105, 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.

1 520,405,105
-1 -520,405,105

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 520,405,105.

Example:
1 x 520,405,105 = 520,405,105
and
-1 x -520,405,105 = 520,405,105
Notice both answers equal 520,405,105

With that explanation out of the way, let's continue. Next, we take the number 520,405,105 and divide it by 2:

520,405,105 ÷ 2 = 260,202,552.5

If the quotient is a whole number, then 2 and 260,202,552.5 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:

1 520,405,105
-1 -520,405,105

Now, we try dividing 520,405,105 by 3:

520,405,105 ÷ 3 = 173,468,368.3333

If the quotient is a whole number, then 3 and 173,468,368.3333 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:

1 520,405,105
-1 -520,405,105

Let's try dividing by 4:

520,405,105 ÷ 4 = 130,101,276.25

If the quotient is a whole number, then 4 and 130,101,276.25 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:

1 520,405,105
-1 520,405,105
Keep dividing by the next highest number until you cannot divide anymore.

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

1511175585187935556,5832,782,9156,122,4139,461,91130,612,06547,309,555104,081,021520,405,105
-1-5-11-17-55-85-187-935-556,583-2,782,915-6,122,413-9,461,911-30,612,065-47,309,555-104,081,021-520,405,105

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