Q: What are the factor combinations of the number 7,310,501?

 A:
Positive:   1 x 731050111 x 664591127 x 575631397 x 5233
Negative: -1 x -7310501-11 x -664591-127 x -57563-1397 x -5233


How do I find the factor combinations of the number 7,310,501?

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 7,310,501, 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 7,310,501
-1 -7,310,501

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 7,310,501.

Example:
1 x 7,310,501 = 7,310,501
and
-1 x -7,310,501 = 7,310,501
Notice both answers equal 7,310,501

With that explanation out of the way, let's continue. Next, we take the number 7,310,501 and divide it by 2:

7,310,501 ÷ 2 = 3,655,250.5

If the quotient is a whole number, then 2 and 3,655,250.5 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 7,310,501
-1 -7,310,501

Now, we try dividing 7,310,501 by 3:

7,310,501 ÷ 3 = 2,436,833.6667

If the quotient is a whole number, then 3 and 2,436,833.6667 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 7,310,501
-1 -7,310,501

Let's try dividing by 4:

7,310,501 ÷ 4 = 1,827,625.25

If the quotient is a whole number, then 4 and 1,827,625.25 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 7,310,501
-1 7,310,501
Keep dividing by the next highest number until you cannot divide anymore.

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

1111271,3975,23357,563664,5917,310,501
-1-11-127-1,397-5,233-57,563-664,591-7,310,501

More Examples

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