Q: What are the factor combinations of the number 302,004,101?

 A:
Positive:   1 x 3020041017 x 4314344337 x 816227349 x 6163349157 x 1923593259 x 11660391061 x 2846411099 x 2747991813 x 1665775809 x 519897427 x 406637693 x 39257
Negative: -1 x -302004101-7 x -43143443-37 x -8162273-49 x -6163349-157 x -1923593-259 x -1166039-1061 x -284641-1099 x -274799-1813 x -166577-5809 x -51989-7427 x -40663-7693 x -39257


How do I find the factor combinations of the number 302,004,101?

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 302,004,101, 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.

1 302,004,101
-1 -302,004,101

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 302,004,101.

Example:
1 x 302,004,101 = 302,004,101
and
-1 x -302,004,101 = 302,004,101
Notice both answers equal 302,004,101

With that explanation out of the way, let's continue. Next, we take the number 302,004,101 and divide it by 2:

302,004,101 ÷ 2 = 151,002,050.5

If the quotient is a whole number, then 2 and 151,002,050.5 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:

1 302,004,101
-1 -302,004,101

Now, we try dividing 302,004,101 by 3:

302,004,101 ÷ 3 = 100,668,033.6667

If the quotient is a whole number, then 3 and 100,668,033.6667 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:

1 302,004,101
-1 -302,004,101

Let's try dividing by 4:

302,004,101 ÷ 4 = 75,501,025.25

If the quotient is a whole number, then 4 and 75,501,025.25 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:

1 302,004,101
-1 302,004,101
Keep dividing by the next highest number until you cannot divide anymore.

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

1737491572591,0611,0991,8135,8097,4277,69339,25740,66351,989166,577274,799284,6411,166,0391,923,5936,163,3498,162,27343,143,443302,004,101
-1-7-37-49-157-259-1,061-1,099-1,813-5,809-7,427-7,693-39,257-40,663-51,989-166,577-274,799-284,641-1,166,039-1,923,593-6,163,349-8,162,273-43,143,443-302,004,101

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