Q: What are the factor combinations of the number 1,421,609?

 A:
Positive:   1 x 14216097 x 20308729 x 4902147 x 30247149 x 9541203 x 7003329 x 43211043 x 1363
Negative: -1 x -1421609-7 x -203087-29 x -49021-47 x -30247-149 x -9541-203 x -7003-329 x -4321-1043 x -1363


How do I find the factor combinations of the number 1,421,609?

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 1,421,609, 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 1,421,609
-1 -1,421,609

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 1,421,609.

Example:
1 x 1,421,609 = 1,421,609
and
-1 x -1,421,609 = 1,421,609
Notice both answers equal 1,421,609

With that explanation out of the way, let's continue. Next, we take the number 1,421,609 and divide it by 2:

1,421,609 ÷ 2 = 710,804.5

If the quotient is a whole number, then 2 and 710,804.5 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 1,421,609
-1 -1,421,609

Now, we try dividing 1,421,609 by 3:

1,421,609 ÷ 3 = 473,869.6667

If the quotient is a whole number, then 3 and 473,869.6667 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 1,421,609
-1 -1,421,609

Let's try dividing by 4:

1,421,609 ÷ 4 = 355,402.25

If the quotient is a whole number, then 4 and 355,402.25 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 1,421,609
-1 1,421,609
Keep dividing by the next highest number until you cannot divide anymore.

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

1729471492033291,0431,3634,3217,0039,54130,24749,021203,0871,421,609
-1-7-29-47-149-203-329-1,043-1,363-4,321-7,003-9,541-30,247-49,021-203,087-1,421,609

More Examples

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