Q: What are the factor combinations of the number 72,705,217?

 A:
Positive:   1 x 7270521713 x 559270943 x 1690819113 x 643409559 x 1300631151 x 631671469 x 494934859 x 14963
Negative: -1 x -72705217-13 x -5592709-43 x -1690819-113 x -643409-559 x -130063-1151 x -63167-1469 x -49493-4859 x -14963


How do I find the factor combinations of the number 72,705,217?

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 72,705,217, 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 72,705,217
-1 -72,705,217

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 72,705,217.

Example:
1 x 72,705,217 = 72,705,217
and
-1 x -72,705,217 = 72,705,217
Notice both answers equal 72,705,217

With that explanation out of the way, let's continue. Next, we take the number 72,705,217 and divide it by 2:

72,705,217 ÷ 2 = 36,352,608.5

If the quotient is a whole number, then 2 and 36,352,608.5 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 72,705,217
-1 -72,705,217

Now, we try dividing 72,705,217 by 3:

72,705,217 ÷ 3 = 24,235,072.3333

If the quotient is a whole number, then 3 and 24,235,072.3333 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 72,705,217
-1 -72,705,217

Let's try dividing by 4:

72,705,217 ÷ 4 = 18,176,304.25

If the quotient is a whole number, then 4 and 18,176,304.25 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 72,705,217
-1 72,705,217
Keep dividing by the next highest number until you cannot divide anymore.

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

113431135591,1511,4694,85914,96349,49363,167130,063643,4091,690,8195,592,70972,705,217
-1-13-43-113-559-1,151-1,469-4,859-14,963-49,493-63,167-130,063-643,409-1,690,819-5,592,709-72,705,217

More Examples

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