Q: What are the factor combinations of the number 42,503,417?

 A:
Positive:   1 x 4250341711 x 386394717 x 250020137 x 1148741187 x 227291407 x 104431629 x 675736143 x 6919
Negative: -1 x -42503417-11 x -3863947-17 x -2500201-37 x -1148741-187 x -227291-407 x -104431-629 x -67573-6143 x -6919


How do I find the factor combinations of the number 42,503,417?

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 42,503,417, 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 42,503,417
-1 -42,503,417

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 42,503,417.

Example:
1 x 42,503,417 = 42,503,417
and
-1 x -42,503,417 = 42,503,417
Notice both answers equal 42,503,417

With that explanation out of the way, let's continue. Next, we take the number 42,503,417 and divide it by 2:

42,503,417 ÷ 2 = 21,251,708.5

If the quotient is a whole number, then 2 and 21,251,708.5 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 42,503,417
-1 -42,503,417

Now, we try dividing 42,503,417 by 3:

42,503,417 ÷ 3 = 14,167,805.6667

If the quotient is a whole number, then 3 and 14,167,805.6667 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 42,503,417
-1 -42,503,417

Let's try dividing by 4:

42,503,417 ÷ 4 = 10,625,854.25

If the quotient is a whole number, then 4 and 10,625,854.25 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 42,503,417
-1 42,503,417
Keep dividing by the next highest number until you cannot divide anymore.

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

11117371874076296,1436,91967,573104,431227,2911,148,7412,500,2013,863,94742,503,417
-1-11-17-37-187-407-629-6,143-6,919-67,573-104,431-227,291-1,148,741-2,500,201-3,863,947-42,503,417

More Examples

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