Q: What are the factor combinations of the number 123,002,196?

 A:
Positive:   1 x 1230021962 x 615010983 x 410007324 x 307505496 x 2050036612 x 1025018347 x 261706894 x 1308534141 x 872356188 x 654267282 x 436178467 x 263388564 x 218089934 x 1316941401 x 877961868 x 658472802 x 438985604 x 21949
Negative: -1 x -123002196-2 x -61501098-3 x -41000732-4 x -30750549-6 x -20500366-12 x -10250183-47 x -2617068-94 x -1308534-141 x -872356-188 x -654267-282 x -436178-467 x -263388-564 x -218089-934 x -131694-1401 x -87796-1868 x -65847-2802 x -43898-5604 x -21949


How do I find the factor combinations of the number 123,002,196?

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 123,002,196, 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.

1 123,002,196
-1 -123,002,196

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 123,002,196.

Example:
1 x 123,002,196 = 123,002,196
and
-1 x -123,002,196 = 123,002,196
Notice both answers equal 123,002,196

With that explanation out of the way, let's continue. Next, we take the number 123,002,196 and divide it by 2:

123,002,196 ÷ 2 = 61,501,098

If the quotient is a whole number, then 2 and 61,501,098 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 61,501,098 123,002,196
-1 -2 -61,501,098 -123,002,196

Now, we try dividing 123,002,196 by 3:

123,002,196 ÷ 3 = 41,000,732

If the quotient is a whole number, then 3 and 41,000,732 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 41,000,732 61,501,098 123,002,196
-1 -2 -3 -41,000,732 -61,501,098 -123,002,196

Let's try dividing by 4:

123,002,196 ÷ 4 = 30,750,549

If the quotient is a whole number, then 4 and 30,750,549 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 30,750,549 41,000,732 61,501,098 123,002,196
-1 -2 -3 -4 -30,750,549 -41,000,732 -61,501,098 123,002,196
Keep dividing by the next highest number until you cannot divide anymore.

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

123461247941411882824675649341,4011,8682,8025,60421,94943,89865,84787,796131,694218,089263,388436,178654,267872,3561,308,5342,617,06810,250,18320,500,36630,750,54941,000,73261,501,098123,002,196
-1-2-3-4-6-12-47-94-141-188-282-467-564-934-1,401-1,868-2,802-5,604-21,949-43,898-65,847-87,796-131,694-218,089-263,388-436,178-654,267-872,356-1,308,534-2,617,068-10,250,183-20,500,366-30,750,549-41,000,732-61,501,098-123,002,196

More Examples

Here are some more numbers to try:

123,002,194123,002,195123,002,197123,002,198
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