Q: What are the factor combinations of the number 42,256,123?

 A:
Positive:   1 x 422561237 x 603658913 x 325047173 x 57885191 x 464353511 x 82693949 x 445276361 x 6643
Negative: -1 x -42256123-7 x -6036589-13 x -3250471-73 x -578851-91 x -464353-511 x -82693-949 x -44527-6361 x -6643


How do I find the factor combinations of the number 42,256,123?

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 42,256,123, 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 42,256,123
-1 -42,256,123

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 42,256,123.

Example:
1 x 42,256,123 = 42,256,123
and
-1 x -42,256,123 = 42,256,123
Notice both answers equal 42,256,123

With that explanation out of the way, let's continue. Next, we take the number 42,256,123 and divide it by 2:

42,256,123 ÷ 2 = 21,128,061.5

If the quotient is a whole number, then 2 and 21,128,061.5 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 42,256,123
-1 -42,256,123

Now, we try dividing 42,256,123 by 3:

42,256,123 ÷ 3 = 14,085,374.3333

If the quotient is a whole number, then 3 and 14,085,374.3333 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 42,256,123
-1 -42,256,123

Let's try dividing by 4:

42,256,123 ÷ 4 = 10,564,030.75

If the quotient is a whole number, then 4 and 10,564,030.75 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 42,256,123
-1 42,256,123
Keep dividing by the next highest number until you cannot divide anymore.

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

171373915119496,3616,64344,52782,693464,353578,8513,250,4716,036,58942,256,123
-1-7-13-73-91-511-949-6,361-6,643-44,527-82,693-464,353-578,851-3,250,471-6,036,589-42,256,123

More Examples

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