Q: What are the factor combinations of the number 103,022,123?

 A:
Positive:   1 x 10302212319 x 542221729 x 3552487181 x 569183551 x 1869731033 x 997313439 x 299575249 x 19627
Negative: -1 x -103022123-19 x -5422217-29 x -3552487-181 x -569183-551 x -186973-1033 x -99731-3439 x -29957-5249 x -19627


How do I find the factor combinations of the number 103,022,123?

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 103,022,123, 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.

1 103,022,123
-1 -103,022,123

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 103,022,123.

Example:
1 x 103,022,123 = 103,022,123
and
-1 x -103,022,123 = 103,022,123
Notice both answers equal 103,022,123

With that explanation out of the way, let's continue. Next, we take the number 103,022,123 and divide it by 2:

103,022,123 ÷ 2 = 51,511,061.5

If the quotient is a whole number, then 2 and 51,511,061.5 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:

1 103,022,123
-1 -103,022,123

Now, we try dividing 103,022,123 by 3:

103,022,123 ÷ 3 = 34,340,707.6667

If the quotient is a whole number, then 3 and 34,340,707.6667 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:

1 103,022,123
-1 -103,022,123

Let's try dividing by 4:

103,022,123 ÷ 4 = 25,755,530.75

If the quotient is a whole number, then 4 and 25,755,530.75 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:

1 103,022,123
-1 103,022,123
Keep dividing by the next highest number until you cannot divide anymore.

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

119291815511,0333,4395,24919,62729,95799,731186,973569,1833,552,4875,422,217103,022,123
-1-19-29-181-551-1,033-3,439-5,249-19,627-29,957-99,731-186,973-569,183-3,552,487-5,422,217-103,022,123

More Examples

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