Q: What are the factor combinations of the number 102,121,123?

 A:
Positive:   1 x 10212112313 x 7855471169 x 604267593 x 1722111019 x 1002177709 x 13247
Negative: -1 x -102121123-13 x -7855471-169 x -604267-593 x -172211-1019 x -100217-7709 x -13247


How do I find the factor combinations of the number 102,121,123?

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 102,121,123, 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.

1 102,121,123
-1 -102,121,123

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 102,121,123.

Example:
1 x 102,121,123 = 102,121,123
and
-1 x -102,121,123 = 102,121,123
Notice both answers equal 102,121,123

With that explanation out of the way, let's continue. Next, we take the number 102,121,123 and divide it by 2:

102,121,123 ÷ 2 = 51,060,561.5

If the quotient is a whole number, then 2 and 51,060,561.5 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:

1 102,121,123
-1 -102,121,123

Now, we try dividing 102,121,123 by 3:

102,121,123 ÷ 3 = 34,040,374.3333

If the quotient is a whole number, then 3 and 34,040,374.3333 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:

1 102,121,123
-1 -102,121,123

Let's try dividing by 4:

102,121,123 ÷ 4 = 25,530,280.75

If the quotient is a whole number, then 4 and 25,530,280.75 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:

1 102,121,123
-1 102,121,123
Keep dividing by the next highest number until you cannot divide anymore.

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

1131695931,0197,70913,247100,217172,211604,2677,855,471102,121,123
-1-13-169-593-1,019-7,709-13,247-100,217-172,211-604,267-7,855,471-102,121,123

More Examples

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