Q: What are the factor combinations of the number 72,202,117?

 A:
Positive:   1 x 7220211713 x 555400943 x 1679119227 x 318071559 x 129163569 x 1268932951 x 244677397 x 9761
Negative: -1 x -72202117-13 x -5554009-43 x -1679119-227 x -318071-559 x -129163-569 x -126893-2951 x -24467-7397 x -9761


How do I find the factor combinations of the number 72,202,117?

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 72,202,117, 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 72,202,117
-1 -72,202,117

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 72,202,117.

Example:
1 x 72,202,117 = 72,202,117
and
-1 x -72,202,117 = 72,202,117
Notice both answers equal 72,202,117

With that explanation out of the way, let's continue. Next, we take the number 72,202,117 and divide it by 2:

72,202,117 ÷ 2 = 36,101,058.5

If the quotient is a whole number, then 2 and 36,101,058.5 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 72,202,117
-1 -72,202,117

Now, we try dividing 72,202,117 by 3:

72,202,117 ÷ 3 = 24,067,372.3333

If the quotient is a whole number, then 3 and 24,067,372.3333 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 72,202,117
-1 -72,202,117

Let's try dividing by 4:

72,202,117 ÷ 4 = 18,050,529.25

If the quotient is a whole number, then 4 and 18,050,529.25 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 72,202,117
-1 72,202,117
Keep dividing by the next highest number until you cannot divide anymore.

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

113432275595692,9517,3979,76124,467126,893129,163318,0711,679,1195,554,00972,202,117
-1-13-43-227-559-569-2,951-7,397-9,761-24,467-126,893-129,163-318,071-1,679,119-5,554,009-72,202,117

More Examples

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