Q: What are the factor combinations of the number 732,612?

 A:
Positive:   1 x 7326122 x 3663063 x 2442044 x 1831536 x 12210212 x 61051
Negative: -1 x -732612-2 x -366306-3 x -244204-4 x -183153-6 x -122102-12 x -61051


How do I find the factor combinations of the number 732,612?

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 732,612, 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.

1 732,612
-1 -732,612

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 732,612.

Example:
1 x 732,612 = 732,612
and
-1 x -732,612 = 732,612
Notice both answers equal 732,612

With that explanation out of the way, let's continue. Next, we take the number 732,612 and divide it by 2:

732,612 ÷ 2 = 366,306

If the quotient is a whole number, then 2 and 366,306 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 2 366,306 732,612
-1 -2 -366,306 -732,612

Now, we try dividing 732,612 by 3:

732,612 ÷ 3 = 244,204

If the quotient is a whole number, then 3 and 244,204 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 3 244,204 366,306 732,612
-1 -2 -3 -244,204 -366,306 -732,612

Let's try dividing by 4:

732,612 ÷ 4 = 183,153

If the quotient is a whole number, then 4 and 183,153 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 4 183,153 244,204 366,306 732,612
-1 -2 -3 -4 -183,153 -244,204 -366,306 732,612
Keep dividing by the next highest number until you cannot divide anymore.

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

123461261,051122,102183,153244,204366,306732,612
-1-2-3-4-6-12-61,051-122,102-183,153-244,204-366,306-732,612

More Examples

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