Q: What are the factor combinations of the number 653,028?

 A:
Positive:   1 x 6530282 x 3265143 x 2176764 x 1632576 x 10883812 x 54419
Negative: -1 x -653028-2 x -326514-3 x -217676-4 x -163257-6 x -108838-12 x -54419


How do I find the factor combinations of the number 653,028?

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 653,028, 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.

1 653,028
-1 -653,028

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 653,028.

Example:
1 x 653,028 = 653,028
and
-1 x -653,028 = 653,028
Notice both answers equal 653,028

With that explanation out of the way, let's continue. Next, we take the number 653,028 and divide it by 2:

653,028 ÷ 2 = 326,514

If the quotient is a whole number, then 2 and 326,514 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 2 326,514 653,028
-1 -2 -326,514 -653,028

Now, we try dividing 653,028 by 3:

653,028 ÷ 3 = 217,676

If the quotient is a whole number, then 3 and 217,676 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 3 217,676 326,514 653,028
-1 -2 -3 -217,676 -326,514 -653,028

Let's try dividing by 4:

653,028 ÷ 4 = 163,257

If the quotient is a whole number, then 4 and 163,257 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 4 163,257 217,676 326,514 653,028
-1 -2 -3 -4 -163,257 -217,676 -326,514 653,028
Keep dividing by the next highest number until you cannot divide anymore.

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

123461254,419108,838163,257217,676326,514653,028
-1-2-3-4-6-12-54,419-108,838-163,257-217,676-326,514-653,028

More Examples

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