Q: What are the factor combinations of the number 516,564,169?

 A:
Positive:   1 x 51656416911 x 4696037947 x 10990727517 x 999157821 x 6291891217 x 4244579031 x 5719913387 x 38587
Negative: -1 x -516564169-11 x -46960379-47 x -10990727-517 x -999157-821 x -629189-1217 x -424457-9031 x -57199-13387 x -38587


How do I find the factor combinations of the number 516,564,169?

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 516,564,169, 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.

1 516,564,169
-1 -516,564,169

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 516,564,169.

Example:
1 x 516,564,169 = 516,564,169
and
-1 x -516,564,169 = 516,564,169
Notice both answers equal 516,564,169

With that explanation out of the way, let's continue. Next, we take the number 516,564,169 and divide it by 2:

516,564,169 ÷ 2 = 258,282,084.5

If the quotient is a whole number, then 2 and 258,282,084.5 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:

1 516,564,169
-1 -516,564,169

Now, we try dividing 516,564,169 by 3:

516,564,169 ÷ 3 = 172,188,056.3333

If the quotient is a whole number, then 3 and 172,188,056.3333 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:

1 516,564,169
-1 -516,564,169

Let's try dividing by 4:

516,564,169 ÷ 4 = 129,141,042.25

If the quotient is a whole number, then 4 and 129,141,042.25 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:

1 516,564,169
-1 516,564,169
Keep dividing by the next highest number until you cannot divide anymore.

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

111475178211,2179,03113,38738,58757,199424,457629,189999,15710,990,72746,960,379516,564,169
-1-11-47-517-821-1,217-9,031-13,387-38,587-57,199-424,457-629,189-999,157-10,990,727-46,960,379-516,564,169

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