Q: What are the factor combinations of the number 130,145,021?

 A:
Positive:   1 x 13014502137 x 351743347 x 276904367 x 19424631117 x 1165131739 x 748392479 x 524993149 x 41329
Negative: -1 x -130145021-37 x -3517433-47 x -2769043-67 x -1942463-1117 x -116513-1739 x -74839-2479 x -52499-3149 x -41329


How do I find the factor combinations of the number 130,145,021?

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 130,145,021, 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.

1 130,145,021
-1 -130,145,021

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 130,145,021.

Example:
1 x 130,145,021 = 130,145,021
and
-1 x -130,145,021 = 130,145,021
Notice both answers equal 130,145,021

With that explanation out of the way, let's continue. Next, we take the number 130,145,021 and divide it by 2:

130,145,021 ÷ 2 = 65,072,510.5

If the quotient is a whole number, then 2 and 65,072,510.5 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:

1 130,145,021
-1 -130,145,021

Now, we try dividing 130,145,021 by 3:

130,145,021 ÷ 3 = 43,381,673.6667

If the quotient is a whole number, then 3 and 43,381,673.6667 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:

1 130,145,021
-1 -130,145,021

Let's try dividing by 4:

130,145,021 ÷ 4 = 32,536,255.25

If the quotient is a whole number, then 4 and 32,536,255.25 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:

1 130,145,021
-1 130,145,021
Keep dividing by the next highest number until you cannot divide anymore.

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

13747671,1171,7392,4793,14941,32952,49974,839116,5131,942,4632,769,0433,517,433130,145,021
-1-37-47-67-1,117-1,739-2,479-3,149-41,329-52,499-74,839-116,513-1,942,463-2,769,043-3,517,433-130,145,021

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