Q: What are the factor combinations of the number 3,523,807?

 A:
Positive:   1 x 35238077 x 50340123 x 15320943 x 81949161 x 21887301 x 11707509 x 6923989 x 3563
Negative: -1 x -3523807-7 x -503401-23 x -153209-43 x -81949-161 x -21887-301 x -11707-509 x -6923-989 x -3563


How do I find the factor combinations of the number 3,523,807?

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 3,523,807, 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 3,523,807
-1 -3,523,807

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 3,523,807.

Example:
1 x 3,523,807 = 3,523,807
and
-1 x -3,523,807 = 3,523,807
Notice both answers equal 3,523,807

With that explanation out of the way, let's continue. Next, we take the number 3,523,807 and divide it by 2:

3,523,807 ÷ 2 = 1,761,903.5

If the quotient is a whole number, then 2 and 1,761,903.5 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 3,523,807
-1 -3,523,807

Now, we try dividing 3,523,807 by 3:

3,523,807 ÷ 3 = 1,174,602.3333

If the quotient is a whole number, then 3 and 1,174,602.3333 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 3,523,807
-1 -3,523,807

Let's try dividing by 4:

3,523,807 ÷ 4 = 880,951.75

If the quotient is a whole number, then 4 and 880,951.75 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 3,523,807
-1 3,523,807
Keep dividing by the next highest number until you cannot divide anymore.

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

1723431613015099893,5636,92311,70721,88781,949153,209503,4013,523,807
-1-7-23-43-161-301-509-989-3,563-6,923-11,707-21,887-81,949-153,209-503,401-3,523,807

More Examples

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