Q: What are the factor combinations of the number 5,136,131?

 A:
Positive:   1 x 51361317 x 73373311 x 46692113 x 39508749 x 10481977 x 6670391 x 56441143 x 35917539 x 9529637 x 8063733 x 70071001 x 5131
Negative: -1 x -5136131-7 x -733733-11 x -466921-13 x -395087-49 x -104819-77 x -66703-91 x -56441-143 x -35917-539 x -9529-637 x -8063-733 x -7007-1001 x -5131


How do I find the factor combinations of the number 5,136,131?

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 5,136,131, 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 5,136,131
-1 -5,136,131

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 5,136,131.

Example:
1 x 5,136,131 = 5,136,131
and
-1 x -5,136,131 = 5,136,131
Notice both answers equal 5,136,131

With that explanation out of the way, let's continue. Next, we take the number 5,136,131 and divide it by 2:

5,136,131 ÷ 2 = 2,568,065.5

If the quotient is a whole number, then 2 and 2,568,065.5 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 5,136,131
-1 -5,136,131

Now, we try dividing 5,136,131 by 3:

5,136,131 ÷ 3 = 1,712,043.6667

If the quotient is a whole number, then 3 and 1,712,043.6667 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 5,136,131
-1 -5,136,131

Let's try dividing by 4:

5,136,131 ÷ 4 = 1,284,032.75

If the quotient is a whole number, then 4 and 1,284,032.75 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 5,136,131
-1 5,136,131
Keep dividing by the next highest number until you cannot divide anymore.

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

1711134977911435396377331,0015,1317,0078,0639,52935,91756,44166,703104,819395,087466,921733,7335,136,131
-1-7-11-13-49-77-91-143-539-637-733-1,001-5,131-7,007-8,063-9,529-35,917-56,441-66,703-104,819-395,087-466,921-733,733-5,136,131

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