Q: What are the factor combinations of the number 103,011,503?

 A:
Positive:   1 x 1030115037 x 1471592923 x 4478761161 x 639823331 x 3112131933 x 532912317 x 444597613 x 13531
Negative: -1 x -103011503-7 x -14715929-23 x -4478761-161 x -639823-331 x -311213-1933 x -53291-2317 x -44459-7613 x -13531


How do I find the factor combinations of the number 103,011,503?

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 103,011,503, 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.

1 103,011,503
-1 -103,011,503

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 103,011,503.

Example:
1 x 103,011,503 = 103,011,503
and
-1 x -103,011,503 = 103,011,503
Notice both answers equal 103,011,503

With that explanation out of the way, let's continue. Next, we take the number 103,011,503 and divide it by 2:

103,011,503 ÷ 2 = 51,505,751.5

If the quotient is a whole number, then 2 and 51,505,751.5 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:

1 103,011,503
-1 -103,011,503

Now, we try dividing 103,011,503 by 3:

103,011,503 ÷ 3 = 34,337,167.6667

If the quotient is a whole number, then 3 and 34,337,167.6667 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:

1 103,011,503
-1 -103,011,503

Let's try dividing by 4:

103,011,503 ÷ 4 = 25,752,875.75

If the quotient is a whole number, then 4 and 25,752,875.75 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:

1 103,011,503
-1 103,011,503
Keep dividing by the next highest number until you cannot divide anymore.

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

17231613311,9332,3177,61313,53144,45953,291311,213639,8234,478,76114,715,929103,011,503
-1-7-23-161-331-1,933-2,317-7,613-13,531-44,459-53,291-311,213-639,823-4,478,761-14,715,929-103,011,503

More Examples

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