Q: What are the factor combinations of the number 67,181,867?

 A:
Positive:   1 x 6718186731 x 216715743 x 1562369101 x 665167499 x 1346331333 x 503993131 x 214574343 x 15469
Negative: -1 x -67181867-31 x -2167157-43 x -1562369-101 x -665167-499 x -134633-1333 x -50399-3131 x -21457-4343 x -15469


How do I find the factor combinations of the number 67,181,867?

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 67,181,867, 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 67,181,867
-1 -67,181,867

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 67,181,867.

Example:
1 x 67,181,867 = 67,181,867
and
-1 x -67,181,867 = 67,181,867
Notice both answers equal 67,181,867

With that explanation out of the way, let's continue. Next, we take the number 67,181,867 and divide it by 2:

67,181,867 ÷ 2 = 33,590,933.5

If the quotient is a whole number, then 2 and 33,590,933.5 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 67,181,867
-1 -67,181,867

Now, we try dividing 67,181,867 by 3:

67,181,867 ÷ 3 = 22,393,955.6667

If the quotient is a whole number, then 3 and 22,393,955.6667 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 67,181,867
-1 -67,181,867

Let's try dividing by 4:

67,181,867 ÷ 4 = 16,795,466.75

If the quotient is a whole number, then 4 and 16,795,466.75 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 67,181,867
-1 67,181,867
Keep dividing by the next highest number until you cannot divide anymore.

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

131431014991,3333,1314,34315,46921,45750,399134,633665,1671,562,3692,167,15767,181,867
-1-31-43-101-499-1,333-3,131-4,343-15,469-21,457-50,399-134,633-665,167-1,562,369-2,167,157-67,181,867

More Examples

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