Q: What are the factor combinations of the number 84,016,723?

 A:
Positive:   1 x 840167237 x 1200238923 x 365290149 x 1714627127 x 661549161 x 521843587 x 143129889 x 945071127 x 745492921 x 287634109 x 204476223 x 13501
Negative: -1 x -84016723-7 x -12002389-23 x -3652901-49 x -1714627-127 x -661549-161 x -521843-587 x -143129-889 x -94507-1127 x -74549-2921 x -28763-4109 x -20447-6223 x -13501


How do I find the factor combinations of the number 84,016,723?

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 84,016,723, 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 84,016,723
-1 -84,016,723

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 84,016,723.

Example:
1 x 84,016,723 = 84,016,723
and
-1 x -84,016,723 = 84,016,723
Notice both answers equal 84,016,723

With that explanation out of the way, let's continue. Next, we take the number 84,016,723 and divide it by 2:

84,016,723 ÷ 2 = 42,008,361.5

If the quotient is a whole number, then 2 and 42,008,361.5 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 84,016,723
-1 -84,016,723

Now, we try dividing 84,016,723 by 3:

84,016,723 ÷ 3 = 28,005,574.3333

If the quotient is a whole number, then 3 and 28,005,574.3333 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 84,016,723
-1 -84,016,723

Let's try dividing by 4:

84,016,723 ÷ 4 = 21,004,180.75

If the quotient is a whole number, then 4 and 21,004,180.75 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 84,016,723
-1 84,016,723
Keep dividing by the next highest number until you cannot divide anymore.

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

1723491271615878891,1272,9214,1096,22313,50120,44728,76374,54994,507143,129521,843661,5491,714,6273,652,90112,002,38984,016,723
-1-7-23-49-127-161-587-889-1,127-2,921-4,109-6,223-13,501-20,447-28,763-74,549-94,507-143,129-521,843-661,549-1,714,627-3,652,901-12,002,389-84,016,723

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