Q: What are the factor combinations of the number 407,726,015?

 A:
Positive:   1 x 4077260155 x 81545203103 x 3958505515 x 791701619 x 6586851279 x 3187853095 x 1317376395 x 63757
Negative: -1 x -407726015-5 x -81545203-103 x -3958505-515 x -791701-619 x -658685-1279 x -318785-3095 x -131737-6395 x -63757


How do I find the factor combinations of the number 407,726,015?

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 407,726,015, 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.

1 407,726,015
-1 -407,726,015

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 407,726,015.

Example:
1 x 407,726,015 = 407,726,015
and
-1 x -407,726,015 = 407,726,015
Notice both answers equal 407,726,015

With that explanation out of the way, let's continue. Next, we take the number 407,726,015 and divide it by 2:

407,726,015 ÷ 2 = 203,863,007.5

If the quotient is a whole number, then 2 and 203,863,007.5 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:

1 407,726,015
-1 -407,726,015

Now, we try dividing 407,726,015 by 3:

407,726,015 ÷ 3 = 135,908,671.6667

If the quotient is a whole number, then 3 and 135,908,671.6667 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:

1 407,726,015
-1 -407,726,015

Let's try dividing by 4:

407,726,015 ÷ 4 = 101,931,503.75

If the quotient is a whole number, then 4 and 101,931,503.75 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:

1 407,726,015
-1 407,726,015
Keep dividing by the next highest number until you cannot divide anymore.

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

151035156191,2793,0956,39563,757131,737318,785658,685791,7013,958,50581,545,203407,726,015
-1-5-103-515-619-1,279-3,095-6,395-63,757-131,737-318,785-658,685-791,701-3,958,505-81,545,203-407,726,015

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