Q: What are the factor combinations of the number 85,321,973?

 A:
Positive:   1 x 8532197311 x 775654323 x 370965129 x 2942137253 x 337241319 x 267467401 x 212773667 x 127919841 x 1014534411 x 193437337 x 116299223 x 9251
Negative: -1 x -85321973-11 x -7756543-23 x -3709651-29 x -2942137-253 x -337241-319 x -267467-401 x -212773-667 x -127919-841 x -101453-4411 x -19343-7337 x -11629-9223 x -9251


How do I find the factor combinations of the number 85,321,973?

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 85,321,973, 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 85,321,973
-1 -85,321,973

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 85,321,973.

Example:
1 x 85,321,973 = 85,321,973
and
-1 x -85,321,973 = 85,321,973
Notice both answers equal 85,321,973

With that explanation out of the way, let's continue. Next, we take the number 85,321,973 and divide it by 2:

85,321,973 ÷ 2 = 42,660,986.5

If the quotient is a whole number, then 2 and 42,660,986.5 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 85,321,973
-1 -85,321,973

Now, we try dividing 85,321,973 by 3:

85,321,973 ÷ 3 = 28,440,657.6667

If the quotient is a whole number, then 3 and 28,440,657.6667 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 85,321,973
-1 -85,321,973

Let's try dividing by 4:

85,321,973 ÷ 4 = 21,330,493.25

If the quotient is a whole number, then 4 and 21,330,493.25 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 85,321,973
-1 85,321,973
Keep dividing by the next highest number until you cannot divide anymore.

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

11123292533194016678414,4117,3379,2239,25111,62919,343101,453127,919212,773267,467337,2412,942,1373,709,6517,756,54385,321,973
-1-11-23-29-253-319-401-667-841-4,411-7,337-9,223-9,251-11,629-19,343-101,453-127,919-212,773-267,467-337,241-2,942,137-3,709,651-7,756,543-85,321,973

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