Q: What are the factor combinations of the number 4,741,735?

 A:
Positive:   1 x 47417355 x 94834719 x 24956537 x 12815571 x 6678595 x 49913185 x 25631355 x 13357361 x 13135703 x 67451349 x 35151805 x 2627
Negative: -1 x -4741735-5 x -948347-19 x -249565-37 x -128155-71 x -66785-95 x -49913-185 x -25631-355 x -13357-361 x -13135-703 x -6745-1349 x -3515-1805 x -2627


How do I find the factor combinations of the number 4,741,735?

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 4,741,735, 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 4,741,735
-1 -4,741,735

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 4,741,735.

Example:
1 x 4,741,735 = 4,741,735
and
-1 x -4,741,735 = 4,741,735
Notice both answers equal 4,741,735

With that explanation out of the way, let's continue. Next, we take the number 4,741,735 and divide it by 2:

4,741,735 ÷ 2 = 2,370,867.5

If the quotient is a whole number, then 2 and 2,370,867.5 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 4,741,735
-1 -4,741,735

Now, we try dividing 4,741,735 by 3:

4,741,735 ÷ 3 = 1,580,578.3333

If the quotient is a whole number, then 3 and 1,580,578.3333 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 4,741,735
-1 -4,741,735

Let's try dividing by 4:

4,741,735 ÷ 4 = 1,185,433.75

If the quotient is a whole number, then 4 and 1,185,433.75 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 4,741,735
-1 4,741,735
Keep dividing by the next highest number until you cannot divide anymore.

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

15193771951853553617031,3491,8052,6273,5156,74513,13513,35725,63149,91366,785128,155249,565948,3474,741,735
-1-5-19-37-71-95-185-355-361-703-1,349-1,805-2,627-3,515-6,745-13,135-13,357-25,631-49,913-66,785-128,155-249,565-948,347-4,741,735

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