Q: What are the factor combinations of the number 4,002,215?

 A:
Positive:   1 x 40022155 x 8004437 x 57174535 x 11434941 x 97615205 x 19523287 x 139451435 x 2789
Negative: -1 x -4002215-5 x -800443-7 x -571745-35 x -114349-41 x -97615-205 x -19523-287 x -13945-1435 x -2789


How do I find the factor combinations of the number 4,002,215?

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 4,002,215, 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 4,002,215
-1 -4,002,215

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 4,002,215.

Example:
1 x 4,002,215 = 4,002,215
and
-1 x -4,002,215 = 4,002,215
Notice both answers equal 4,002,215

With that explanation out of the way, let's continue. Next, we take the number 4,002,215 and divide it by 2:

4,002,215 ÷ 2 = 2,001,107.5

If the quotient is a whole number, then 2 and 2,001,107.5 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 4,002,215
-1 -4,002,215

Now, we try dividing 4,002,215 by 3:

4,002,215 ÷ 3 = 1,334,071.6667

If the quotient is a whole number, then 3 and 1,334,071.6667 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 4,002,215
-1 -4,002,215

Let's try dividing by 4:

4,002,215 ÷ 4 = 1,000,553.75

If the quotient is a whole number, then 4 and 1,000,553.75 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 4,002,215
-1 4,002,215
Keep dividing by the next highest number until you cannot divide anymore.

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

15735412052871,4352,78913,94519,52397,615114,349571,745800,4434,002,215
-1-5-7-35-41-205-287-1,435-2,789-13,945-19,523-97,615-114,349-571,745-800,443-4,002,215

More Examples

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