Q: What are the factor combinations of the number 42,340,123?

 A:
Positive:   1 x 423401237 x 6048589179 x 2365371253 x 33791
Negative: -1 x -42340123-7 x -6048589-179 x -236537-1253 x -33791


How do I find the factor combinations of the number 42,340,123?

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 42,340,123, 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 42,340,123
-1 -42,340,123

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 42,340,123.

Example:
1 x 42,340,123 = 42,340,123
and
-1 x -42,340,123 = 42,340,123
Notice both answers equal 42,340,123

With that explanation out of the way, let's continue. Next, we take the number 42,340,123 and divide it by 2:

42,340,123 ÷ 2 = 21,170,061.5

If the quotient is a whole number, then 2 and 21,170,061.5 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 42,340,123
-1 -42,340,123

Now, we try dividing 42,340,123 by 3:

42,340,123 ÷ 3 = 14,113,374.3333

If the quotient is a whole number, then 3 and 14,113,374.3333 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 42,340,123
-1 -42,340,123

Let's try dividing by 4:

42,340,123 ÷ 4 = 10,585,030.75

If the quotient is a whole number, then 4 and 10,585,030.75 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 42,340,123
-1 42,340,123
Keep dividing by the next highest number until you cannot divide anymore.

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

171791,25333,791236,5376,048,58942,340,123
-1-7-179-1,253-33,791-236,537-6,048,589-42,340,123

More Examples

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