Q: What are the factor combinations of the number 42,301,223?

 A:
Positive:   1 x 42301223227 x 186349307 x 137789607 x 69689
Negative: -1 x -42301223-227 x -186349-307 x -137789-607 x -69689


How do I find the factor combinations of the number 42,301,223?

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 42,301,223, 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 42,301,223
-1 -42,301,223

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 42,301,223.

Example:
1 x 42,301,223 = 42,301,223
and
-1 x -42,301,223 = 42,301,223
Notice both answers equal 42,301,223

With that explanation out of the way, let's continue. Next, we take the number 42,301,223 and divide it by 2:

42,301,223 ÷ 2 = 21,150,611.5

If the quotient is a whole number, then 2 and 21,150,611.5 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 42,301,223
-1 -42,301,223

Now, we try dividing 42,301,223 by 3:

42,301,223 ÷ 3 = 14,100,407.6667

If the quotient is a whole number, then 3 and 14,100,407.6667 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 42,301,223
-1 -42,301,223

Let's try dividing by 4:

42,301,223 ÷ 4 = 10,575,305.75

If the quotient is a whole number, then 4 and 10,575,305.75 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 42,301,223
-1 42,301,223
Keep dividing by the next highest number until you cannot divide anymore.

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

122730760769,689137,789186,34942,301,223
-1-227-307-607-69,689-137,789-186,349-42,301,223

More Examples

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