Q: What are the factor combinations of the number 304,151,137?

 A:
Positive:   1 x 30415113731 x 981132737 x 8220301283 x 1074739937 x 3246011147 x 2651718773 x 3466910471 x 29047
Negative: -1 x -304151137-31 x -9811327-37 x -8220301-283 x -1074739-937 x -324601-1147 x -265171-8773 x -34669-10471 x -29047


How do I find the factor combinations of the number 304,151,137?

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 304,151,137, 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.

1 304,151,137
-1 -304,151,137

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 304,151,137.

Example:
1 x 304,151,137 = 304,151,137
and
-1 x -304,151,137 = 304,151,137
Notice both answers equal 304,151,137

With that explanation out of the way, let's continue. Next, we take the number 304,151,137 and divide it by 2:

304,151,137 ÷ 2 = 152,075,568.5

If the quotient is a whole number, then 2 and 152,075,568.5 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:

1 304,151,137
-1 -304,151,137

Now, we try dividing 304,151,137 by 3:

304,151,137 ÷ 3 = 101,383,712.3333

If the quotient is a whole number, then 3 and 101,383,712.3333 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:

1 304,151,137
-1 -304,151,137

Let's try dividing by 4:

304,151,137 ÷ 4 = 76,037,784.25

If the quotient is a whole number, then 4 and 76,037,784.25 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:

1 304,151,137
-1 304,151,137
Keep dividing by the next highest number until you cannot divide anymore.

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

131372839371,1478,77310,47129,04734,669265,171324,6011,074,7398,220,3019,811,327304,151,137
-1-31-37-283-937-1,147-8,773-10,471-29,047-34,669-265,171-324,601-1,074,739-8,220,301-9,811,327-304,151,137

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