Q: What are the factor combinations of the number 500,350,541?

 A:
Positive:   1 x 50035054119 x 2633423973 x 685411797 x 51582531387 x 3607431843 x 2714873719 x 1345397081 x 70661
Negative: -1 x -500350541-19 x -26334239-73 x -6854117-97 x -5158253-1387 x -360743-1843 x -271487-3719 x -134539-7081 x -70661


How do I find the factor combinations of the number 500,350,541?

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 500,350,541, 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.

1 500,350,541
-1 -500,350,541

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 500,350,541.

Example:
1 x 500,350,541 = 500,350,541
and
-1 x -500,350,541 = 500,350,541
Notice both answers equal 500,350,541

With that explanation out of the way, let's continue. Next, we take the number 500,350,541 and divide it by 2:

500,350,541 ÷ 2 = 250,175,270.5

If the quotient is a whole number, then 2 and 250,175,270.5 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:

1 500,350,541
-1 -500,350,541

Now, we try dividing 500,350,541 by 3:

500,350,541 ÷ 3 = 166,783,513.6667

If the quotient is a whole number, then 3 and 166,783,513.6667 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:

1 500,350,541
-1 -500,350,541

Let's try dividing by 4:

500,350,541 ÷ 4 = 125,087,635.25

If the quotient is a whole number, then 4 and 125,087,635.25 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:

1 500,350,541
-1 500,350,541
Keep dividing by the next highest number until you cannot divide anymore.

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

11973971,3871,8433,7197,08170,661134,539271,487360,7435,158,2536,854,11726,334,239500,350,541
-1-19-73-97-1,387-1,843-3,719-7,081-70,661-134,539-271,487-360,743-5,158,253-6,854,117-26,334,239-500,350,541

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