Q: What are the factor combinations of the number 31,302,101?

 A:
Positive:   1 x 3130210119 x 164747989 x 351709107 x 292543173 x 1809371691 x 185112033 x 153973287 x 9523
Negative: -1 x -31302101-19 x -1647479-89 x -351709-107 x -292543-173 x -180937-1691 x -18511-2033 x -15397-3287 x -9523


How do I find the factor combinations of the number 31,302,101?

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 31,302,101, 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 31,302,101
-1 -31,302,101

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 31,302,101.

Example:
1 x 31,302,101 = 31,302,101
and
-1 x -31,302,101 = 31,302,101
Notice both answers equal 31,302,101

With that explanation out of the way, let's continue. Next, we take the number 31,302,101 and divide it by 2:

31,302,101 ÷ 2 = 15,651,050.5

If the quotient is a whole number, then 2 and 15,651,050.5 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 31,302,101
-1 -31,302,101

Now, we try dividing 31,302,101 by 3:

31,302,101 ÷ 3 = 10,434,033.6667

If the quotient is a whole number, then 3 and 10,434,033.6667 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 31,302,101
-1 -31,302,101

Let's try dividing by 4:

31,302,101 ÷ 4 = 7,825,525.25

If the quotient is a whole number, then 4 and 7,825,525.25 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 31,302,101
-1 31,302,101
Keep dividing by the next highest number until you cannot divide anymore.

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

119891071731,6912,0333,2879,52315,39718,511180,937292,543351,7091,647,47931,302,101
-1-19-89-107-173-1,691-2,033-3,287-9,523-15,397-18,511-180,937-292,543-351,709-1,647,479-31,302,101

More Examples

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