Q: What are the factor combinations of the number 3,520,205?

 A:
Positive:   1 x 35202055 x 70404113 x 27078531 x 11355565 x 54157155 x 22711403 x 87351747 x 2015
Negative: -1 x -3520205-5 x -704041-13 x -270785-31 x -113555-65 x -54157-155 x -22711-403 x -8735-1747 x -2015


How do I find the factor combinations of the number 3,520,205?

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 3,520,205, 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 3,520,205
-1 -3,520,205

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 3,520,205.

Example:
1 x 3,520,205 = 3,520,205
and
-1 x -3,520,205 = 3,520,205
Notice both answers equal 3,520,205

With that explanation out of the way, let's continue. Next, we take the number 3,520,205 and divide it by 2:

3,520,205 ÷ 2 = 1,760,102.5

If the quotient is a whole number, then 2 and 1,760,102.5 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 3,520,205
-1 -3,520,205

Now, we try dividing 3,520,205 by 3:

3,520,205 ÷ 3 = 1,173,401.6667

If the quotient is a whole number, then 3 and 1,173,401.6667 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 3,520,205
-1 -3,520,205

Let's try dividing by 4:

3,520,205 ÷ 4 = 880,051.25

If the quotient is a whole number, then 4 and 880,051.25 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 3,520,205
-1 3,520,205
Keep dividing by the next highest number until you cannot divide anymore.

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

151331651554031,7472,0158,73522,71154,157113,555270,785704,0413,520,205
-1-5-13-31-65-155-403-1,747-2,015-8,735-22,711-54,157-113,555-270,785-704,041-3,520,205

More Examples

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