Q: What are the factor combinations of the number 100,100,124?

 A:
Positive:   1 x 1001001242 x 500500623 x 333667084 x 250250316 x 166833549 x 1112223612 x 834167718 x 556111827 x 370741236 x 278055954 x 185370681 x 1235804108 x 926853162 x 617902324 x 308951
Negative: -1 x -100100124-2 x -50050062-3 x -33366708-4 x -25025031-6 x -16683354-9 x -11122236-12 x -8341677-18 x -5561118-27 x -3707412-36 x -2780559-54 x -1853706-81 x -1235804-108 x -926853-162 x -617902-324 x -308951


How do I find the factor combinations of the number 100,100,124?

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 100,100,124, 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.

1 100,100,124
-1 -100,100,124

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 100,100,124.

Example:
1 x 100,100,124 = 100,100,124
and
-1 x -100,100,124 = 100,100,124
Notice both answers equal 100,100,124

With that explanation out of the way, let's continue. Next, we take the number 100,100,124 and divide it by 2:

100,100,124 ÷ 2 = 50,050,062

If the quotient is a whole number, then 2 and 50,050,062 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 50,050,062 100,100,124
-1 -2 -50,050,062 -100,100,124

Now, we try dividing 100,100,124 by 3:

100,100,124 ÷ 3 = 33,366,708

If the quotient is a whole number, then 3 and 33,366,708 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 33,366,708 50,050,062 100,100,124
-1 -2 -3 -33,366,708 -50,050,062 -100,100,124

Let's try dividing by 4:

100,100,124 ÷ 4 = 25,025,031

If the quotient is a whole number, then 4 and 25,025,031 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 25,025,031 33,366,708 50,050,062 100,100,124
-1 -2 -3 -4 -25,025,031 -33,366,708 -50,050,062 100,100,124
Keep dividing by the next highest number until you cannot divide anymore.

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

123469121827365481108162324308,951617,902926,8531,235,8041,853,7062,780,5593,707,4125,561,1188,341,67711,122,23616,683,35425,025,03133,366,70850,050,062100,100,124
-1-2-3-4-6-9-12-18-27-36-54-81-108-162-324-308,951-617,902-926,853-1,235,804-1,853,706-2,780,559-3,707,412-5,561,118-8,341,677-11,122,236-16,683,354-25,025,031-33,366,708-50,050,062-100,100,124

More Examples

Here are some more numbers to try:

100,100,122100,100,123100,100,125100,100,126
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