Q: What are the factor combinations of the number 675,820?

 A:
Positive:   1 x 6758202 x 3379104 x 1689555 x 13516410 x 6758220 x 33791
Negative: -1 x -675820-2 x -337910-4 x -168955-5 x -135164-10 x -67582-20 x -33791


How do I find the factor combinations of the number 675,820?

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 675,820, 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.

1 675,820
-1 -675,820

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 675,820.

Example:
1 x 675,820 = 675,820
and
-1 x -675,820 = 675,820
Notice both answers equal 675,820

With that explanation out of the way, let's continue. Next, we take the number 675,820 and divide it by 2:

675,820 ÷ 2 = 337,910

If the quotient is a whole number, then 2 and 337,910 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 2 337,910 675,820
-1 -2 -337,910 -675,820

Now, we try dividing 675,820 by 3:

675,820 ÷ 3 = 225,273.3333

If the quotient is a whole number, then 3 and 225,273.3333 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 2 337,910 675,820
-1 -2 -337,910 -675,820

Let's try dividing by 4:

675,820 ÷ 4 = 168,955

If the quotient is a whole number, then 4 and 168,955 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 4 168,955 337,910 675,820
-1 -2 -4 -168,955 -337,910 675,820
Keep dividing by the next highest number until you cannot divide anymore.

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

1245102033,79167,582135,164168,955337,910675,820
-1-2-4-5-10-20-33,791-67,582-135,164-168,955-337,910-675,820

More Examples

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