Q: What are the factor combinations of the number 32,500,501?

 A:
Positive:   1 x 3250050111 x 295459153 x 613217107 x 303743521 x 62381583 x 557471177 x 276135671 x 5731
Negative: -1 x -32500501-11 x -2954591-53 x -613217-107 x -303743-521 x -62381-583 x -55747-1177 x -27613-5671 x -5731


How do I find the factor combinations of the number 32,500,501?

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 32,500,501, 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 32,500,501
-1 -32,500,501

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 32,500,501.

Example:
1 x 32,500,501 = 32,500,501
and
-1 x -32,500,501 = 32,500,501
Notice both answers equal 32,500,501

With that explanation out of the way, let's continue. Next, we take the number 32,500,501 and divide it by 2:

32,500,501 ÷ 2 = 16,250,250.5

If the quotient is a whole number, then 2 and 16,250,250.5 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 32,500,501
-1 -32,500,501

Now, we try dividing 32,500,501 by 3:

32,500,501 ÷ 3 = 10,833,500.3333

If the quotient is a whole number, then 3 and 10,833,500.3333 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 32,500,501
-1 -32,500,501

Let's try dividing by 4:

32,500,501 ÷ 4 = 8,125,125.25

If the quotient is a whole number, then 4 and 8,125,125.25 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 32,500,501
-1 32,500,501
Keep dividing by the next highest number until you cannot divide anymore.

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

111531075215831,1775,6715,73127,61355,74762,381303,743613,2172,954,59132,500,501
-1-11-53-107-521-583-1,177-5,671-5,731-27,613-55,747-62,381-303,743-613,217-2,954,591-32,500,501

More Examples

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