Q: What are the factor combinations of the number 9,698,435?

 A:
Positive:   1 x 96984355 x 193968743 x 22554579 x 122765215 x 45109395 x 24553571 x 169852855 x 3397
Negative: -1 x -9698435-5 x -1939687-43 x -225545-79 x -122765-215 x -45109-395 x -24553-571 x -16985-2855 x -3397


How do I find the factor combinations of the number 9,698,435?

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 9,698,435, 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 9,698,435
-1 -9,698,435

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 9,698,435.

Example:
1 x 9,698,435 = 9,698,435
and
-1 x -9,698,435 = 9,698,435
Notice both answers equal 9,698,435

With that explanation out of the way, let's continue. Next, we take the number 9,698,435 and divide it by 2:

9,698,435 ÷ 2 = 4,849,217.5

If the quotient is a whole number, then 2 and 4,849,217.5 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 9,698,435
-1 -9,698,435

Now, we try dividing 9,698,435 by 3:

9,698,435 ÷ 3 = 3,232,811.6667

If the quotient is a whole number, then 3 and 3,232,811.6667 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 9,698,435
-1 -9,698,435

Let's try dividing by 4:

9,698,435 ÷ 4 = 2,424,608.75

If the quotient is a whole number, then 4 and 2,424,608.75 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 9,698,435
-1 9,698,435
Keep dividing by the next highest number until you cannot divide anymore.

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

1543792153955712,8553,39716,98524,55345,109122,765225,5451,939,6879,698,435
-1-5-43-79-215-395-571-2,855-3,397-16,985-24,553-45,109-122,765-225,545-1,939,687-9,698,435

More Examples

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