Q: What are the factor combinations of the number 510,717,349?

 A:
Positive:   1 x 51071734917 x 3004219767 x 7622647359 x 14226111139 x 4483911249 x 4089016103 x 8368321233 x 24053
Negative: -1 x -510717349-17 x -30042197-67 x -7622647-359 x -1422611-1139 x -448391-1249 x -408901-6103 x -83683-21233 x -24053


How do I find the factor combinations of the number 510,717,349?

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 510,717,349, 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.

1 510,717,349
-1 -510,717,349

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 510,717,349.

Example:
1 x 510,717,349 = 510,717,349
and
-1 x -510,717,349 = 510,717,349
Notice both answers equal 510,717,349

With that explanation out of the way, let's continue. Next, we take the number 510,717,349 and divide it by 2:

510,717,349 ÷ 2 = 255,358,674.5

If the quotient is a whole number, then 2 and 255,358,674.5 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:

1 510,717,349
-1 -510,717,349

Now, we try dividing 510,717,349 by 3:

510,717,349 ÷ 3 = 170,239,116.3333

If the quotient is a whole number, then 3 and 170,239,116.3333 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:

1 510,717,349
-1 -510,717,349

Let's try dividing by 4:

510,717,349 ÷ 4 = 127,679,337.25

If the quotient is a whole number, then 4 and 127,679,337.25 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:

1 510,717,349
-1 510,717,349
Keep dividing by the next highest number until you cannot divide anymore.

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

117673591,1391,2496,10321,23324,05383,683408,901448,3911,422,6117,622,64730,042,197510,717,349
-1-17-67-359-1,139-1,249-6,103-21,233-24,053-83,683-408,901-448,391-1,422,611-7,622,647-30,042,197-510,717,349

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