Q: What are the factor combinations of the number 31,531,501?

 A:
Positive:   1 x 3153150141 x 76906147 x 6708831927 x 16363
Negative: -1 x -31531501-41 x -769061-47 x -670883-1927 x -16363


How do I find the factor combinations of the number 31,531,501?

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 31,531,501, 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 31,531,501
-1 -31,531,501

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 31,531,501.

Example:
1 x 31,531,501 = 31,531,501
and
-1 x -31,531,501 = 31,531,501
Notice both answers equal 31,531,501

With that explanation out of the way, let's continue. Next, we take the number 31,531,501 and divide it by 2:

31,531,501 ÷ 2 = 15,765,750.5

If the quotient is a whole number, then 2 and 15,765,750.5 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 31,531,501
-1 -31,531,501

Now, we try dividing 31,531,501 by 3:

31,531,501 ÷ 3 = 10,510,500.3333

If the quotient is a whole number, then 3 and 10,510,500.3333 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 31,531,501
-1 -31,531,501

Let's try dividing by 4:

31,531,501 ÷ 4 = 7,882,875.25

If the quotient is a whole number, then 4 and 7,882,875.25 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 31,531,501
-1 31,531,501
Keep dividing by the next highest number until you cannot divide anymore.

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

141471,92716,363670,883769,06131,531,501
-1-41-47-1,927-16,363-670,883-769,061-31,531,501

More Examples

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