Q: What are the factor combinations of the number 31,607,773?

 A:
Positive:   1 x 3160777319 x 166356723 x 1374251151 x 209323437 x 72329479 x 659872869 x 110173473 x 9101
Negative: -1 x -31607773-19 x -1663567-23 x -1374251-151 x -209323-437 x -72329-479 x -65987-2869 x -11017-3473 x -9101


How do I find the factor combinations of the number 31,607,773?

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 31,607,773, 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 31,607,773
-1 -31,607,773

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 31,607,773.

Example:
1 x 31,607,773 = 31,607,773
and
-1 x -31,607,773 = 31,607,773
Notice both answers equal 31,607,773

With that explanation out of the way, let's continue. Next, we take the number 31,607,773 and divide it by 2:

31,607,773 ÷ 2 = 15,803,886.5

If the quotient is a whole number, then 2 and 15,803,886.5 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 31,607,773
-1 -31,607,773

Now, we try dividing 31,607,773 by 3:

31,607,773 ÷ 3 = 10,535,924.3333

If the quotient is a whole number, then 3 and 10,535,924.3333 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 31,607,773
-1 -31,607,773

Let's try dividing by 4:

31,607,773 ÷ 4 = 7,901,943.25

If the quotient is a whole number, then 4 and 7,901,943.25 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 31,607,773
-1 31,607,773
Keep dividing by the next highest number until you cannot divide anymore.

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

119231514374792,8693,4739,10111,01765,98772,329209,3231,374,2511,663,56731,607,773
-1-19-23-151-437-479-2,869-3,473-9,101-11,017-65,987-72,329-209,323-1,374,251-1,663,567-31,607,773

More Examples

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