Q: What are the factor combinations of the number 417,804?

 A:
Positive:   1 x 4178042 x 2089023 x 1392684 x 1044516 x 6963412 x 3481737 x 1129274 x 5646111 x 3764148 x 2823222 x 1882444 x 941
Negative: -1 x -417804-2 x -208902-3 x -139268-4 x -104451-6 x -69634-12 x -34817-37 x -11292-74 x -5646-111 x -3764-148 x -2823-222 x -1882-444 x -941


How do I find the factor combinations of the number 417,804?

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 417,804, 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.

1 417,804
-1 -417,804

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 417,804.

Example:
1 x 417,804 = 417,804
and
-1 x -417,804 = 417,804
Notice both answers equal 417,804

With that explanation out of the way, let's continue. Next, we take the number 417,804 and divide it by 2:

417,804 ÷ 2 = 208,902

If the quotient is a whole number, then 2 and 208,902 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 2 208,902 417,804
-1 -2 -208,902 -417,804

Now, we try dividing 417,804 by 3:

417,804 ÷ 3 = 139,268

If the quotient is a whole number, then 3 and 139,268 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 3 139,268 208,902 417,804
-1 -2 -3 -139,268 -208,902 -417,804

Let's try dividing by 4:

417,804 ÷ 4 = 104,451

If the quotient is a whole number, then 4 and 104,451 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 4 104,451 139,268 208,902 417,804
-1 -2 -3 -4 -104,451 -139,268 -208,902 417,804
Keep dividing by the next highest number until you cannot divide anymore.

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

123461237741111482224449411,8822,8233,7645,64611,29234,81769,634104,451139,268208,902417,804
-1-2-3-4-6-12-37-74-111-148-222-444-941-1,882-2,823-3,764-5,646-11,292-34,817-69,634-104,451-139,268-208,902-417,804

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