Q: What are the factor combinations of the number 31,251,635?

 A:
Positive:   1 x 312516355 x 625032741 x 762235157 x 199055205 x 152447785 x 39811971 x 321854855 x 6437
Negative: -1 x -31251635-5 x -6250327-41 x -762235-157 x -199055-205 x -152447-785 x -39811-971 x -32185-4855 x -6437


How do I find the factor combinations of the number 31,251,635?

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 31,251,635, 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 31,251,635
-1 -31,251,635

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 31,251,635.

Example:
1 x 31,251,635 = 31,251,635
and
-1 x -31,251,635 = 31,251,635
Notice both answers equal 31,251,635

With that explanation out of the way, let's continue. Next, we take the number 31,251,635 and divide it by 2:

31,251,635 ÷ 2 = 15,625,817.5

If the quotient is a whole number, then 2 and 15,625,817.5 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 31,251,635
-1 -31,251,635

Now, we try dividing 31,251,635 by 3:

31,251,635 ÷ 3 = 10,417,211.6667

If the quotient is a whole number, then 3 and 10,417,211.6667 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 31,251,635
-1 -31,251,635

Let's try dividing by 4:

31,251,635 ÷ 4 = 7,812,908.75

If the quotient is a whole number, then 4 and 7,812,908.75 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 31,251,635
-1 31,251,635
Keep dividing by the next highest number until you cannot divide anymore.

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

15411572057859714,8556,43732,18539,811152,447199,055762,2356,250,32731,251,635
-1-5-41-157-205-785-971-4,855-6,437-32,185-39,811-152,447-199,055-762,235-6,250,327-31,251,635

More Examples

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