Q: What are the factor combinations of the number 301,737,709?

 A:
Positive:   1 x 3017377097 x 4310538713 x 2321059317 x 1774927791 x 3315799119 x 2535611221 x 13653291547 x 195047
Negative: -1 x -301737709-7 x -43105387-13 x -23210593-17 x -17749277-91 x -3315799-119 x -2535611-221 x -1365329-1547 x -195047


How do I find the factor combinations of the number 301,737,709?

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 301,737,709, 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.

1 301,737,709
-1 -301,737,709

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 301,737,709.

Example:
1 x 301,737,709 = 301,737,709
and
-1 x -301,737,709 = 301,737,709
Notice both answers equal 301,737,709

With that explanation out of the way, let's continue. Next, we take the number 301,737,709 and divide it by 2:

301,737,709 ÷ 2 = 150,868,854.5

If the quotient is a whole number, then 2 and 150,868,854.5 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:

1 301,737,709
-1 -301,737,709

Now, we try dividing 301,737,709 by 3:

301,737,709 ÷ 3 = 100,579,236.3333

If the quotient is a whole number, then 3 and 100,579,236.3333 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:

1 301,737,709
-1 -301,737,709

Let's try dividing by 4:

301,737,709 ÷ 4 = 75,434,427.25

If the quotient is a whole number, then 4 and 75,434,427.25 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:

1 301,737,709
-1 301,737,709
Keep dividing by the next highest number until you cannot divide anymore.

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

171317911192211,547195,0471,365,3292,535,6113,315,79917,749,27723,210,59343,105,387301,737,709
-1-7-13-17-91-119-221-1,547-195,047-1,365,329-2,535,611-3,315,799-17,749,277-23,210,593-43,105,387-301,737,709

More Examples

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