Q: What are the factor combinations of the number 413,241,355?

 A:
Positive:   1 x 4132413555 x 8264827117 x 2430831519 x 2174954585 x 486166395 x 4349909323 x 12793851615 x 255877
Negative: -1 x -413241355-5 x -82648271-17 x -24308315-19 x -21749545-85 x -4861663-95 x -4349909-323 x -1279385-1615 x -255877


How do I find the factor combinations of the number 413,241,355?

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 413,241,355, 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.

1 413,241,355
-1 -413,241,355

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 413,241,355.

Example:
1 x 413,241,355 = 413,241,355
and
-1 x -413,241,355 = 413,241,355
Notice both answers equal 413,241,355

With that explanation out of the way, let's continue. Next, we take the number 413,241,355 and divide it by 2:

413,241,355 ÷ 2 = 206,620,677.5

If the quotient is a whole number, then 2 and 206,620,677.5 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:

1 413,241,355
-1 -413,241,355

Now, we try dividing 413,241,355 by 3:

413,241,355 ÷ 3 = 137,747,118.3333

If the quotient is a whole number, then 3 and 137,747,118.3333 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:

1 413,241,355
-1 -413,241,355

Let's try dividing by 4:

413,241,355 ÷ 4 = 103,310,338.75

If the quotient is a whole number, then 4 and 103,310,338.75 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:

1 413,241,355
-1 413,241,355
Keep dividing by the next highest number until you cannot divide anymore.

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

15171985953231,615255,8771,279,3854,349,9094,861,66321,749,54524,308,31582,648,271413,241,355
-1-5-17-19-85-95-323-1,615-255,877-1,279,385-4,349,909-4,861,663-21,749,545-24,308,315-82,648,271-413,241,355

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