Q: What are the factor combinations of the number 71,348,123?

 A:
Positive:   1 x 713481237 x 1019258911 x 648619353 x 134619177 x 926599371 x 192313583 x 1223814081 x 17483
Negative: -1 x -71348123-7 x -10192589-11 x -6486193-53 x -1346191-77 x -926599-371 x -192313-583 x -122381-4081 x -17483


How do I find the factor combinations of the number 71,348,123?

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 71,348,123, 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 71,348,123
-1 -71,348,123

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 71,348,123.

Example:
1 x 71,348,123 = 71,348,123
and
-1 x -71,348,123 = 71,348,123
Notice both answers equal 71,348,123

With that explanation out of the way, let's continue. Next, we take the number 71,348,123 and divide it by 2:

71,348,123 ÷ 2 = 35,674,061.5

If the quotient is a whole number, then 2 and 35,674,061.5 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 71,348,123
-1 -71,348,123

Now, we try dividing 71,348,123 by 3:

71,348,123 ÷ 3 = 23,782,707.6667

If the quotient is a whole number, then 3 and 23,782,707.6667 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 71,348,123
-1 -71,348,123

Let's try dividing by 4:

71,348,123 ÷ 4 = 17,837,030.75

If the quotient is a whole number, then 4 and 17,837,030.75 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 71,348,123
-1 71,348,123
Keep dividing by the next highest number until you cannot divide anymore.

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

171153773715834,08117,483122,381192,313926,5991,346,1916,486,19310,192,58971,348,123
-1-7-11-53-77-371-583-4,081-17,483-122,381-192,313-926,599-1,346,191-6,486,193-10,192,589-71,348,123

More Examples

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