Q: What are the factor combinations of the number 1,522,165?

 A:
Positive:   1 x 15221655 x 304433
Negative: -1 x -1522165-5 x -304433


How do I find the factor combinations of the number 1,522,165?

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 1,522,165, 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 1,522,165
-1 -1,522,165

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 1,522,165.

Example:
1 x 1,522,165 = 1,522,165
and
-1 x -1,522,165 = 1,522,165
Notice both answers equal 1,522,165

With that explanation out of the way, let's continue. Next, we take the number 1,522,165 and divide it by 2:

1,522,165 ÷ 2 = 761,082.5

If the quotient is a whole number, then 2 and 761,082.5 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 1,522,165
-1 -1,522,165

Now, we try dividing 1,522,165 by 3:

1,522,165 ÷ 3 = 507,388.3333

If the quotient is a whole number, then 3 and 507,388.3333 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 1,522,165
-1 -1,522,165

Let's try dividing by 4:

1,522,165 ÷ 4 = 380,541.25

If the quotient is a whole number, then 4 and 380,541.25 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 1,522,165
-1 1,522,165
Keep dividing by the next highest number until you cannot divide anymore.

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

15304,4331,522,165
-1-5-304,433-1,522,165

More Examples

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