Q: What are the factor combinations of the number 302,023,105?

 A:
Positive:   1 x 3020231055 x 6040462117 x 1776606585 x 3553213239 x 12636951195 x 2527394063 x 7433514867 x 20315
Negative: -1 x -302023105-5 x -60404621-17 x -17766065-85 x -3553213-239 x -1263695-1195 x -252739-4063 x -74335-14867 x -20315


How do I find the factor combinations of the number 302,023,105?

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 302,023,105, 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.

1 302,023,105
-1 -302,023,105

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 302,023,105.

Example:
1 x 302,023,105 = 302,023,105
and
-1 x -302,023,105 = 302,023,105
Notice both answers equal 302,023,105

With that explanation out of the way, let's continue. Next, we take the number 302,023,105 and divide it by 2:

302,023,105 ÷ 2 = 151,011,552.5

If the quotient is a whole number, then 2 and 151,011,552.5 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:

1 302,023,105
-1 -302,023,105

Now, we try dividing 302,023,105 by 3:

302,023,105 ÷ 3 = 100,674,368.3333

If the quotient is a whole number, then 3 and 100,674,368.3333 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:

1 302,023,105
-1 -302,023,105

Let's try dividing by 4:

302,023,105 ÷ 4 = 75,505,776.25

If the quotient is a whole number, then 4 and 75,505,776.25 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:

1 302,023,105
-1 302,023,105
Keep dividing by the next highest number until you cannot divide anymore.

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

1517852391,1954,06314,86720,31574,335252,7391,263,6953,553,21317,766,06560,404,621302,023,105
-1-5-17-85-239-1,195-4,063-14,867-20,315-74,335-252,739-1,263,695-3,553,213-17,766,065-60,404,621-302,023,105

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