Q: What are the factor combinations of the number 652,728?

 A:
Positive:   1 x 6527282 x 3263643 x 2175764 x 1631826 x 1087888 x 8159112 x 5439424 x 27197
Negative: -1 x -652728-2 x -326364-3 x -217576-4 x -163182-6 x -108788-8 x -81591-12 x -54394-24 x -27197


How do I find the factor combinations of the number 652,728?

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 652,728, 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.

1 652,728
-1 -652,728

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 652,728.

Example:
1 x 652,728 = 652,728
and
-1 x -652,728 = 652,728
Notice both answers equal 652,728

With that explanation out of the way, let's continue. Next, we take the number 652,728 and divide it by 2:

652,728 ÷ 2 = 326,364

If the quotient is a whole number, then 2 and 326,364 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 2 326,364 652,728
-1 -2 -326,364 -652,728

Now, we try dividing 652,728 by 3:

652,728 ÷ 3 = 217,576

If the quotient is a whole number, then 3 and 217,576 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 3 217,576 326,364 652,728
-1 -2 -3 -217,576 -326,364 -652,728

Let's try dividing by 4:

652,728 ÷ 4 = 163,182

If the quotient is a whole number, then 4 and 163,182 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 4 163,182 217,576 326,364 652,728
-1 -2 -3 -4 -163,182 -217,576 -326,364 652,728
Keep dividing by the next highest number until you cannot divide anymore.

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

123468122427,19754,39481,591108,788163,182217,576326,364652,728
-1-2-3-4-6-8-12-24-27,197-54,394-81,591-108,788-163,182-217,576-326,364-652,728

More Examples

Here are some more numbers to try:

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