Q: What are the factor combinations of the number 556,689?

 A:
Positive:   1 x 5566893 x 1855637 x 7952721 x 2650949 x 11361147 x 3787343 x 1623541 x 1029
Negative: -1 x -556689-3 x -185563-7 x -79527-21 x -26509-49 x -11361-147 x -3787-343 x -1623-541 x -1029


How do I find the factor combinations of the number 556,689?

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 556,689, 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.

1 556,689
-1 -556,689

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 556,689.

Example:
1 x 556,689 = 556,689
and
-1 x -556,689 = 556,689
Notice both answers equal 556,689

With that explanation out of the way, let's continue. Next, we take the number 556,689 and divide it by 2:

556,689 ÷ 2 = 278,344.5

If the quotient is a whole number, then 2 and 278,344.5 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:

1 556,689
-1 -556,689

Now, we try dividing 556,689 by 3:

556,689 ÷ 3 = 185,563

If the quotient is a whole number, then 3 and 185,563 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 3 185,563 556,689
-1 -3 -185,563 -556,689

Let's try dividing by 4:

556,689 ÷ 4 = 139,172.25

If the quotient is a whole number, then 4 and 139,172.25 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 3 185,563 556,689
-1 -3 -185,563 556,689
Keep dividing by the next highest number until you cannot divide anymore.

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

13721491473435411,0291,6233,78711,36126,50979,527185,563556,689
-1-3-7-21-49-147-343-541-1,029-1,623-3,787-11,361-26,509-79,527-185,563-556,689

More Examples

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