Q: What are the factor combinations of the number 628,068?

 A:
Positive:   1 x 6280682 x 3140343 x 2093564 x 1570176 x 1046787 x 8972412 x 5233914 x 4486221 x 2990828 x 2243142 x 1495484 x 7477
Negative: -1 x -628068-2 x -314034-3 x -209356-4 x -157017-6 x -104678-7 x -89724-12 x -52339-14 x -44862-21 x -29908-28 x -22431-42 x -14954-84 x -7477


How do I find the factor combinations of the number 628,068?

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 628,068, 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.

1 628,068
-1 -628,068

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 628,068.

Example:
1 x 628,068 = 628,068
and
-1 x -628,068 = 628,068
Notice both answers equal 628,068

With that explanation out of the way, let's continue. Next, we take the number 628,068 and divide it by 2:

628,068 ÷ 2 = 314,034

If the quotient is a whole number, then 2 and 314,034 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 2 314,034 628,068
-1 -2 -314,034 -628,068

Now, we try dividing 628,068 by 3:

628,068 ÷ 3 = 209,356

If the quotient is a whole number, then 3 and 209,356 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 3 209,356 314,034 628,068
-1 -2 -3 -209,356 -314,034 -628,068

Let's try dividing by 4:

628,068 ÷ 4 = 157,017

If the quotient is a whole number, then 4 and 157,017 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 4 157,017 209,356 314,034 628,068
-1 -2 -3 -4 -157,017 -209,356 -314,034 628,068
Keep dividing by the next highest number until you cannot divide anymore.

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

1234671214212842847,47714,95422,43129,90844,86252,33989,724104,678157,017209,356314,034628,068
-1-2-3-4-6-7-12-14-21-28-42-84-7,477-14,954-22,431-29,908-44,862-52,339-89,724-104,678-157,017-209,356-314,034-628,068

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