Q: What are the factor combinations of the number 31,192,297?

 A:
Positive:   1 x 3119229717 x 183484159 x 528683137 x 227681227 x 1374111003 x 310992329 x 133933859 x 8083
Negative: -1 x -31192297-17 x -1834841-59 x -528683-137 x -227681-227 x -137411-1003 x -31099-2329 x -13393-3859 x -8083


How do I find the factor combinations of the number 31,192,297?

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 31,192,297, 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 31,192,297
-1 -31,192,297

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 31,192,297.

Example:
1 x 31,192,297 = 31,192,297
and
-1 x -31,192,297 = 31,192,297
Notice both answers equal 31,192,297

With that explanation out of the way, let's continue. Next, we take the number 31,192,297 and divide it by 2:

31,192,297 ÷ 2 = 15,596,148.5

If the quotient is a whole number, then 2 and 15,596,148.5 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 31,192,297
-1 -31,192,297

Now, we try dividing 31,192,297 by 3:

31,192,297 ÷ 3 = 10,397,432.3333

If the quotient is a whole number, then 3 and 10,397,432.3333 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 31,192,297
-1 -31,192,297

Let's try dividing by 4:

31,192,297 ÷ 4 = 7,798,074.25

If the quotient is a whole number, then 4 and 7,798,074.25 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 31,192,297
-1 31,192,297
Keep dividing by the next highest number until you cannot divide anymore.

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

117591372271,0032,3293,8598,08313,39331,099137,411227,681528,6831,834,84131,192,297
-1-17-59-137-227-1,003-2,329-3,859-8,083-13,393-31,099-137,411-227,681-528,683-1,834,841-31,192,297

More Examples

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