Q: What are the factor combinations of the number 1,408,921?

 A:
Positive:   1 x 1408921971 x 1451
Negative: -1 x -1408921-971 x -1451


How do I find the factor combinations of the number 1,408,921?

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 1,408,921, 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 1,408,921
-1 -1,408,921

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 1,408,921.

Example:
1 x 1,408,921 = 1,408,921
and
-1 x -1,408,921 = 1,408,921
Notice both answers equal 1,408,921

With that explanation out of the way, let's continue. Next, we take the number 1,408,921 and divide it by 2:

1,408,921 ÷ 2 = 704,460.5

If the quotient is a whole number, then 2 and 704,460.5 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 1,408,921
-1 -1,408,921

Now, we try dividing 1,408,921 by 3:

1,408,921 ÷ 3 = 469,640.3333

If the quotient is a whole number, then 3 and 469,640.3333 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 1,408,921
-1 -1,408,921

Let's try dividing by 4:

1,408,921 ÷ 4 = 352,230.25

If the quotient is a whole number, then 4 and 352,230.25 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 1,408,921
-1 1,408,921
Keep dividing by the next highest number until you cannot divide anymore.

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

19711,4511,408,921
-1-971-1,451-1,408,921

More Examples

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