Q: What are the factor combinations of the number 418,949?

 A:
Positive:   1 x 41894943 x 9743
Negative: -1 x -418949-43 x -9743


How do I find the factor combinations of the number 418,949?

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 418,949, 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.

1 418,949
-1 -418,949

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 418,949.

Example:
1 x 418,949 = 418,949
and
-1 x -418,949 = 418,949
Notice both answers equal 418,949

With that explanation out of the way, let's continue. Next, we take the number 418,949 and divide it by 2:

418,949 ÷ 2 = 209,474.5

If the quotient is a whole number, then 2 and 209,474.5 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:

1 418,949
-1 -418,949

Now, we try dividing 418,949 by 3:

418,949 ÷ 3 = 139,649.6667

If the quotient is a whole number, then 3 and 139,649.6667 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:

1 418,949
-1 -418,949

Let's try dividing by 4:

418,949 ÷ 4 = 104,737.25

If the quotient is a whole number, then 4 and 104,737.25 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:

1 418,949
-1 418,949
Keep dividing by the next highest number until you cannot divide anymore.

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

1439,743418,949
-1-43-9,743-418,949

More Examples

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