Q: What are the factor combinations of the number 629,898?

 A:
Positive:   1 x 6298982 x 3149493 x 2099666 x 104983277 x 2274379 x 1662554 x 1137758 x 831
Negative: -1 x -629898-2 x -314949-3 x -209966-6 x -104983-277 x -2274-379 x -1662-554 x -1137-758 x -831


How do I find the factor combinations of the number 629,898?

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 629,898, 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.

1 629,898
-1 -629,898

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 629,898.

Example:
1 x 629,898 = 629,898
and
-1 x -629,898 = 629,898
Notice both answers equal 629,898

With that explanation out of the way, let's continue. Next, we take the number 629,898 and divide it by 2:

629,898 ÷ 2 = 314,949

If the quotient is a whole number, then 2 and 314,949 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 314,949 629,898
-1 -2 -314,949 -629,898

Now, we try dividing 629,898 by 3:

629,898 ÷ 3 = 209,966

If the quotient is a whole number, then 3 and 209,966 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 209,966 314,949 629,898
-1 -2 -3 -209,966 -314,949 -629,898

Let's try dividing by 4:

629,898 ÷ 4 = 157,474.5

If the quotient is a whole number, then 4 and 157,474.5 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 2 3 209,966 314,949 629,898
-1 -2 -3 -209,966 -314,949 629,898
Keep dividing by the next highest number until you cannot divide anymore.

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

12362773795547588311,1371,6622,274104,983209,966314,949629,898
-1-2-3-6-277-379-554-758-831-1,137-1,662-2,274-104,983-209,966-314,949-629,898

More Examples

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