Q: What are the factor combinations of the number 7,708,001?

 A:
Positive:   1 x 77080017 x 1101143
Negative: -1 x -7708001-7 x -1101143


How do I find the factor combinations of the number 7,708,001?

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 7,708,001, 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 7,708,001
-1 -7,708,001

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 7,708,001.

Example:
1 x 7,708,001 = 7,708,001
and
-1 x -7,708,001 = 7,708,001
Notice both answers equal 7,708,001

With that explanation out of the way, let's continue. Next, we take the number 7,708,001 and divide it by 2:

7,708,001 ÷ 2 = 3,854,000.5

If the quotient is a whole number, then 2 and 3,854,000.5 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 7,708,001
-1 -7,708,001

Now, we try dividing 7,708,001 by 3:

7,708,001 ÷ 3 = 2,569,333.6667

If the quotient is a whole number, then 3 and 2,569,333.6667 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 7,708,001
-1 -7,708,001

Let's try dividing by 4:

7,708,001 ÷ 4 = 1,927,000.25

If the quotient is a whole number, then 4 and 1,927,000.25 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 7,708,001
-1 7,708,001
Keep dividing by the next highest number until you cannot divide anymore.

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

171,101,1437,708,001
-1-7-1,101,143-7,708,001

More Examples

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