Q: What are the factor combinations of the number 52,123,513?

 A:
Positive:   1 x 5212351313 x 400950117 x 3066089221 x 235853227 x 2296191039 x 501672951 x 176633859 x 13507
Negative: -1 x -52123513-13 x -4009501-17 x -3066089-221 x -235853-227 x -229619-1039 x -50167-2951 x -17663-3859 x -13507


How do I find the factor combinations of the number 52,123,513?

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 52,123,513, 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 52,123,513
-1 -52,123,513

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 52,123,513.

Example:
1 x 52,123,513 = 52,123,513
and
-1 x -52,123,513 = 52,123,513
Notice both answers equal 52,123,513

With that explanation out of the way, let's continue. Next, we take the number 52,123,513 and divide it by 2:

52,123,513 ÷ 2 = 26,061,756.5

If the quotient is a whole number, then 2 and 26,061,756.5 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 52,123,513
-1 -52,123,513

Now, we try dividing 52,123,513 by 3:

52,123,513 ÷ 3 = 17,374,504.3333

If the quotient is a whole number, then 3 and 17,374,504.3333 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 52,123,513
-1 -52,123,513

Let's try dividing by 4:

52,123,513 ÷ 4 = 13,030,878.25

If the quotient is a whole number, then 4 and 13,030,878.25 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 52,123,513
-1 52,123,513
Keep dividing by the next highest number until you cannot divide anymore.

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

113172212271,0392,9513,85913,50717,66350,167229,619235,8533,066,0894,009,50152,123,513
-1-13-17-221-227-1,039-2,951-3,859-13,507-17,663-50,167-229,619-235,853-3,066,089-4,009,501-52,123,513

More Examples

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