Q: What are the factor combinations of the number 305,350,645?

 A:
Positive:   1 x 3053506455 x 6107012923 x 13276115115 x 2655223337 x 9060851685 x 1812177751 x 393957879 x 38755
Negative: -1 x -305350645-5 x -61070129-23 x -13276115-115 x -2655223-337 x -906085-1685 x -181217-7751 x -39395-7879 x -38755


How do I find the factor combinations of the number 305,350,645?

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 305,350,645, 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.

1 305,350,645
-1 -305,350,645

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 305,350,645.

Example:
1 x 305,350,645 = 305,350,645
and
-1 x -305,350,645 = 305,350,645
Notice both answers equal 305,350,645

With that explanation out of the way, let's continue. Next, we take the number 305,350,645 and divide it by 2:

305,350,645 ÷ 2 = 152,675,322.5

If the quotient is a whole number, then 2 and 152,675,322.5 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:

1 305,350,645
-1 -305,350,645

Now, we try dividing 305,350,645 by 3:

305,350,645 ÷ 3 = 101,783,548.3333

If the quotient is a whole number, then 3 and 101,783,548.3333 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:

1 305,350,645
-1 -305,350,645

Let's try dividing by 4:

305,350,645 ÷ 4 = 76,337,661.25

If the quotient is a whole number, then 4 and 76,337,661.25 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:

1 305,350,645
-1 305,350,645
Keep dividing by the next highest number until you cannot divide anymore.

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

15231153371,6857,7517,87938,75539,395181,217906,0852,655,22313,276,11561,070,129305,350,645
-1-5-23-115-337-1,685-7,751-7,879-38,755-39,395-181,217-906,085-2,655,223-13,276,115-61,070,129-305,350,645

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