Q: What are the factor combinations of the number 500,304,233?

 A:
Positive:   1 x 50030423311 x 4548220313 x 38484941143 x 3498631659 x 7591875309 x 942377249 x 690178567 x 58399
Negative: -1 x -500304233-11 x -45482203-13 x -38484941-143 x -3498631-659 x -759187-5309 x -94237-7249 x -69017-8567 x -58399


How do I find the factor combinations of the number 500,304,233?

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 500,304,233, 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.

1 500,304,233
-1 -500,304,233

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 500,304,233.

Example:
1 x 500,304,233 = 500,304,233
and
-1 x -500,304,233 = 500,304,233
Notice both answers equal 500,304,233

With that explanation out of the way, let's continue. Next, we take the number 500,304,233 and divide it by 2:

500,304,233 ÷ 2 = 250,152,116.5

If the quotient is a whole number, then 2 and 250,152,116.5 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:

1 500,304,233
-1 -500,304,233

Now, we try dividing 500,304,233 by 3:

500,304,233 ÷ 3 = 166,768,077.6667

If the quotient is a whole number, then 3 and 166,768,077.6667 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:

1 500,304,233
-1 -500,304,233

Let's try dividing by 4:

500,304,233 ÷ 4 = 125,076,058.25

If the quotient is a whole number, then 4 and 125,076,058.25 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:

1 500,304,233
-1 500,304,233
Keep dividing by the next highest number until you cannot divide anymore.

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

111131436595,3097,2498,56758,39969,01794,237759,1873,498,63138,484,94145,482,203500,304,233
-1-11-13-143-659-5,309-7,249-8,567-58,399-69,017-94,237-759,187-3,498,631-38,484,941-45,482,203-500,304,233

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