Q: What are the factor combinations of the number 72,731,435?

 A:
Positive:   1 x 727314355 x 145462877 x 1039020535 x 207804149 x 1484315245 x 296863343 x 2120451715 x 42409
Negative: -1 x -72731435-5 x -14546287-7 x -10390205-35 x -2078041-49 x -1484315-245 x -296863-343 x -212045-1715 x -42409


How do I find the factor combinations of the number 72,731,435?

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 72,731,435, 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 72,731,435
-1 -72,731,435

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 72,731,435.

Example:
1 x 72,731,435 = 72,731,435
and
-1 x -72,731,435 = 72,731,435
Notice both answers equal 72,731,435

With that explanation out of the way, let's continue. Next, we take the number 72,731,435 and divide it by 2:

72,731,435 ÷ 2 = 36,365,717.5

If the quotient is a whole number, then 2 and 36,365,717.5 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 72,731,435
-1 -72,731,435

Now, we try dividing 72,731,435 by 3:

72,731,435 ÷ 3 = 24,243,811.6667

If the quotient is a whole number, then 3 and 24,243,811.6667 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 72,731,435
-1 -72,731,435

Let's try dividing by 4:

72,731,435 ÷ 4 = 18,182,858.75

If the quotient is a whole number, then 4 and 18,182,858.75 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 72,731,435
-1 72,731,435
Keep dividing by the next highest number until you cannot divide anymore.

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

15735492453431,71542,409212,045296,8631,484,3152,078,04110,390,20514,546,28772,731,435
-1-5-7-35-49-245-343-1,715-42,409-212,045-296,863-1,484,315-2,078,041-10,390,205-14,546,287-72,731,435

More Examples

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