Q: What are the factor combinations of the number 720,855,474?

 A:
Positive:   1 x 7208554742 x 3604277373 x 2402851586 x 12014257971 x 10152894142 x 5076447213 x 3384298426 x 1692149
Negative: -1 x -720855474-2 x -360427737-3 x -240285158-6 x -120142579-71 x -10152894-142 x -5076447-213 x -3384298-426 x -1692149


How do I find the factor combinations of the number 720,855,474?

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 720,855,474, 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.

1 720,855,474
-1 -720,855,474

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 720,855,474.

Example:
1 x 720,855,474 = 720,855,474
and
-1 x -720,855,474 = 720,855,474
Notice both answers equal 720,855,474

With that explanation out of the way, let's continue. Next, we take the number 720,855,474 and divide it by 2:

720,855,474 ÷ 2 = 360,427,737

If the quotient is a whole number, then 2 and 360,427,737 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 2 360,427,737 720,855,474
-1 -2 -360,427,737 -720,855,474

Now, we try dividing 720,855,474 by 3:

720,855,474 ÷ 3 = 240,285,158

If the quotient is a whole number, then 3 and 240,285,158 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 3 240,285,158 360,427,737 720,855,474
-1 -2 -3 -240,285,158 -360,427,737 -720,855,474

Let's try dividing by 4:

720,855,474 ÷ 4 = 180,213,868.5

If the quotient is a whole number, then 4 and 180,213,868.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 2 3 240,285,158 360,427,737 720,855,474
-1 -2 -3 -240,285,158 -360,427,737 720,855,474
Keep dividing by the next highest number until you cannot divide anymore.

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

1236711422134261,692,1493,384,2985,076,44710,152,894120,142,579240,285,158360,427,737720,855,474
-1-2-3-6-71-142-213-426-1,692,149-3,384,298-5,076,447-10,152,894-120,142,579-240,285,158-360,427,737-720,855,474

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