Q: What are the factor combinations of the number 1,968,421?

 A:
Positive:   1 x 19684217 x 28120313 x 15141791 x 2163197 x 20293223 x 8827679 x 28991261 x 1561
Negative: -1 x -1968421-7 x -281203-13 x -151417-91 x -21631-97 x -20293-223 x -8827-679 x -2899-1261 x -1561


How do I find the factor combinations of the number 1,968,421?

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 1,968,421, 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 1,968,421
-1 -1,968,421

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 1,968,421.

Example:
1 x 1,968,421 = 1,968,421
and
-1 x -1,968,421 = 1,968,421
Notice both answers equal 1,968,421

With that explanation out of the way, let's continue. Next, we take the number 1,968,421 and divide it by 2:

1,968,421 ÷ 2 = 984,210.5

If the quotient is a whole number, then 2 and 984,210.5 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 1,968,421
-1 -1,968,421

Now, we try dividing 1,968,421 by 3:

1,968,421 ÷ 3 = 656,140.3333

If the quotient is a whole number, then 3 and 656,140.3333 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 1,968,421
-1 -1,968,421

Let's try dividing by 4:

1,968,421 ÷ 4 = 492,105.25

If the quotient is a whole number, then 4 and 492,105.25 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 1,968,421
-1 1,968,421
Keep dividing by the next highest number until you cannot divide anymore.

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

171391972236791,2611,5612,8998,82720,29321,631151,417281,2031,968,421
-1-7-13-91-97-223-679-1,261-1,561-2,899-8,827-20,293-21,631-151,417-281,203-1,968,421

More Examples

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