Q: What are the factor combinations of the number 41,949,677?

 A:
Positive:   1 x 419496777 x 599281111 x 381360723 x 182389977 x 544801161 x 260557253 x 1658091771 x 23687
Negative: -1 x -41949677-7 x -5992811-11 x -3813607-23 x -1823899-77 x -544801-161 x -260557-253 x -165809-1771 x -23687


How do I find the factor combinations of the number 41,949,677?

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 41,949,677, 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 41,949,677
-1 -41,949,677

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 41,949,677.

Example:
1 x 41,949,677 = 41,949,677
and
-1 x -41,949,677 = 41,949,677
Notice both answers equal 41,949,677

With that explanation out of the way, let's continue. Next, we take the number 41,949,677 and divide it by 2:

41,949,677 ÷ 2 = 20,974,838.5

If the quotient is a whole number, then 2 and 20,974,838.5 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 41,949,677
-1 -41,949,677

Now, we try dividing 41,949,677 by 3:

41,949,677 ÷ 3 = 13,983,225.6667

If the quotient is a whole number, then 3 and 13,983,225.6667 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 41,949,677
-1 -41,949,677

Let's try dividing by 4:

41,949,677 ÷ 4 = 10,487,419.25

If the quotient is a whole number, then 4 and 10,487,419.25 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 41,949,677
-1 41,949,677
Keep dividing by the next highest number until you cannot divide anymore.

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

171123771612531,77123,687165,809260,557544,8011,823,8993,813,6075,992,81141,949,677
-1-7-11-23-77-161-253-1,771-23,687-165,809-260,557-544,801-1,823,899-3,813,607-5,992,811-41,949,677

More Examples

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