Q: What are the factor combinations of the number 53,123,123?

 A:
Positive:   1 x 5312312323 x 230970171 x 7482131633 x 32531
Negative: -1 x -53123123-23 x -2309701-71 x -748213-1633 x -32531


How do I find the factor combinations of the number 53,123,123?

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 53,123,123, 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 53,123,123
-1 -53,123,123

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 53,123,123.

Example:
1 x 53,123,123 = 53,123,123
and
-1 x -53,123,123 = 53,123,123
Notice both answers equal 53,123,123

With that explanation out of the way, let's continue. Next, we take the number 53,123,123 and divide it by 2:

53,123,123 ÷ 2 = 26,561,561.5

If the quotient is a whole number, then 2 and 26,561,561.5 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 53,123,123
-1 -53,123,123

Now, we try dividing 53,123,123 by 3:

53,123,123 ÷ 3 = 17,707,707.6667

If the quotient is a whole number, then 3 and 17,707,707.6667 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 53,123,123
-1 -53,123,123

Let's try dividing by 4:

53,123,123 ÷ 4 = 13,280,780.75

If the quotient is a whole number, then 4 and 13,280,780.75 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 53,123,123
-1 53,123,123
Keep dividing by the next highest number until you cannot divide anymore.

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

123711,63332,531748,2132,309,70153,123,123
-1-23-71-1,633-32,531-748,213-2,309,701-53,123,123

More Examples

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