Q: What are the factor combinations of the number 1,408,015?

 A:
Positive:   1 x 14080155 x 2816037 x 20114535 x 4022949 x 28735245 x 5747343 x 4105821 x 1715
Negative: -1 x -1408015-5 x -281603-7 x -201145-35 x -40229-49 x -28735-245 x -5747-343 x -4105-821 x -1715


How do I find the factor combinations of the number 1,408,015?

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 1,408,015, 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 1,408,015
-1 -1,408,015

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 1,408,015.

Example:
1 x 1,408,015 = 1,408,015
and
-1 x -1,408,015 = 1,408,015
Notice both answers equal 1,408,015

With that explanation out of the way, let's continue. Next, we take the number 1,408,015 and divide it by 2:

1,408,015 ÷ 2 = 704,007.5

If the quotient is a whole number, then 2 and 704,007.5 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 1,408,015
-1 -1,408,015

Now, we try dividing 1,408,015 by 3:

1,408,015 ÷ 3 = 469,338.3333

If the quotient is a whole number, then 3 and 469,338.3333 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 1,408,015
-1 -1,408,015

Let's try dividing by 4:

1,408,015 ÷ 4 = 352,003.75

If the quotient is a whole number, then 4 and 352,003.75 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 1,408,015
-1 1,408,015
Keep dividing by the next highest number until you cannot divide anymore.

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

15735492453438211,7154,1055,74728,73540,229201,145281,6031,408,015
-1-5-7-35-49-245-343-821-1,715-4,105-5,747-28,735-40,229-201,145-281,603-1,408,015

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