Q: What are the factor combinations of the number 720,723,731?

 A:
Positive:   1 x 7207237317 x 10296053313 x 5544028743 x 1676101791 x 7920041301 x 2394431559 x 12893093913 x 184187
Negative: -1 x -720723731-7 x -102960533-13 x -55440287-43 x -16761017-91 x -7920041-301 x -2394431-559 x -1289309-3913 x -184187


How do I find the factor combinations of the number 720,723,731?

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 720,723,731, 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.

1 720,723,731
-1 -720,723,731

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 720,723,731.

Example:
1 x 720,723,731 = 720,723,731
and
-1 x -720,723,731 = 720,723,731
Notice both answers equal 720,723,731

With that explanation out of the way, let's continue. Next, we take the number 720,723,731 and divide it by 2:

720,723,731 ÷ 2 = 360,361,865.5

If the quotient is a whole number, then 2 and 360,361,865.5 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:

1 720,723,731
-1 -720,723,731

Now, we try dividing 720,723,731 by 3:

720,723,731 ÷ 3 = 240,241,243.6667

If the quotient is a whole number, then 3 and 240,241,243.6667 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:

1 720,723,731
-1 -720,723,731

Let's try dividing by 4:

720,723,731 ÷ 4 = 180,180,932.75

If the quotient is a whole number, then 4 and 180,180,932.75 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:

1 720,723,731
-1 720,723,731
Keep dividing by the next highest number until you cannot divide anymore.

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

171343913015593,913184,1871,289,3092,394,4317,920,04116,761,01755,440,287102,960,533720,723,731
-1-7-13-43-91-301-559-3,913-184,187-1,289,309-2,394,431-7,920,041-16,761,017-55,440,287-102,960,533-720,723,731

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