Q: What are the factor combinations of the number 71,423,105?

 A:
Positive:   1 x 714231055 x 1428462113 x 549408565 x 1098817439 x 1626952195 x 325392503 x 285355707 x 12515
Negative: -1 x -71423105-5 x -14284621-13 x -5494085-65 x -1098817-439 x -162695-2195 x -32539-2503 x -28535-5707 x -12515


How do I find the factor combinations of the number 71,423,105?

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 71,423,105, 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 71,423,105
-1 -71,423,105

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 71,423,105.

Example:
1 x 71,423,105 = 71,423,105
and
-1 x -71,423,105 = 71,423,105
Notice both answers equal 71,423,105

With that explanation out of the way, let's continue. Next, we take the number 71,423,105 and divide it by 2:

71,423,105 ÷ 2 = 35,711,552.5

If the quotient is a whole number, then 2 and 35,711,552.5 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 71,423,105
-1 -71,423,105

Now, we try dividing 71,423,105 by 3:

71,423,105 ÷ 3 = 23,807,701.6667

If the quotient is a whole number, then 3 and 23,807,701.6667 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 71,423,105
-1 -71,423,105

Let's try dividing by 4:

71,423,105 ÷ 4 = 17,855,776.25

If the quotient is a whole number, then 4 and 17,855,776.25 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 71,423,105
-1 71,423,105
Keep dividing by the next highest number until you cannot divide anymore.

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

1513654392,1952,5035,70712,51528,53532,539162,6951,098,8175,494,08514,284,62171,423,105
-1-5-13-65-439-2,195-2,503-5,707-12,515-28,535-32,539-162,695-1,098,817-5,494,085-14,284,621-71,423,105

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