Q: What are the factor combinations of the number 41,434,025?

 A:
Positive:   1 x 414340255 x 828680525 x 165736147 x 881575179 x 231475197 x 210325235 x 176315895 x 46295985 x 420651175 x 352634475 x 92594925 x 8413
Negative: -1 x -41434025-5 x -8286805-25 x -1657361-47 x -881575-179 x -231475-197 x -210325-235 x -176315-895 x -46295-985 x -42065-1175 x -35263-4475 x -9259-4925 x -8413


How do I find the factor combinations of the number 41,434,025?

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 41,434,025, 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 41,434,025
-1 -41,434,025

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 41,434,025.

Example:
1 x 41,434,025 = 41,434,025
and
-1 x -41,434,025 = 41,434,025
Notice both answers equal 41,434,025

With that explanation out of the way, let's continue. Next, we take the number 41,434,025 and divide it by 2:

41,434,025 ÷ 2 = 20,717,012.5

If the quotient is a whole number, then 2 and 20,717,012.5 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 41,434,025
-1 -41,434,025

Now, we try dividing 41,434,025 by 3:

41,434,025 ÷ 3 = 13,811,341.6667

If the quotient is a whole number, then 3 and 13,811,341.6667 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 41,434,025
-1 -41,434,025

Let's try dividing by 4:

41,434,025 ÷ 4 = 10,358,506.25

If the quotient is a whole number, then 4 and 10,358,506.25 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 41,434,025
-1 41,434,025
Keep dividing by the next highest number until you cannot divide anymore.

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

1525471791972358959851,1754,4754,9258,4139,25935,26342,06546,295176,315210,325231,475881,5751,657,3618,286,80541,434,025
-1-5-25-47-179-197-235-895-985-1,175-4,475-4,925-8,413-9,259-35,263-42,065-46,295-176,315-210,325-231,475-881,575-1,657,361-8,286,805-41,434,025

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