Q: What are the factor combinations of the number 41,674,321?

 A:
Positive:   1 x 4167432113 x 320571723 x 181192737 x 1126333299 x 139379481 x 86641851 x 489713767 x 11063
Negative: -1 x -41674321-13 x -3205717-23 x -1811927-37 x -1126333-299 x -139379-481 x -86641-851 x -48971-3767 x -11063


How do I find the factor combinations of the number 41,674,321?

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 41,674,321, 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 41,674,321
-1 -41,674,321

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 41,674,321.

Example:
1 x 41,674,321 = 41,674,321
and
-1 x -41,674,321 = 41,674,321
Notice both answers equal 41,674,321

With that explanation out of the way, let's continue. Next, we take the number 41,674,321 and divide it by 2:

41,674,321 ÷ 2 = 20,837,160.5

If the quotient is a whole number, then 2 and 20,837,160.5 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 41,674,321
-1 -41,674,321

Now, we try dividing 41,674,321 by 3:

41,674,321 ÷ 3 = 13,891,440.3333

If the quotient is a whole number, then 3 and 13,891,440.3333 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 41,674,321
-1 -41,674,321

Let's try dividing by 4:

41,674,321 ÷ 4 = 10,418,580.25

If the quotient is a whole number, then 4 and 10,418,580.25 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 41,674,321
-1 41,674,321
Keep dividing by the next highest number until you cannot divide anymore.

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

11323372994818513,76711,06348,97186,641139,3791,126,3331,811,9273,205,71741,674,321
-1-13-23-37-299-481-851-3,767-11,063-48,971-86,641-139,379-1,126,333-1,811,927-3,205,717-41,674,321

More Examples

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