Q: What are the factor combinations of the number 42,020,153?

 A:
Positive:   1 x 420201537 x 600287919 x 2211587133 x 315941193 x 2177211351 x 311031637 x 256693667 x 11459
Negative: -1 x -42020153-7 x -6002879-19 x -2211587-133 x -315941-193 x -217721-1351 x -31103-1637 x -25669-3667 x -11459


How do I find the factor combinations of the number 42,020,153?

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 42,020,153, 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 42,020,153
-1 -42,020,153

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 42,020,153.

Example:
1 x 42,020,153 = 42,020,153
and
-1 x -42,020,153 = 42,020,153
Notice both answers equal 42,020,153

With that explanation out of the way, let's continue. Next, we take the number 42,020,153 and divide it by 2:

42,020,153 ÷ 2 = 21,010,076.5

If the quotient is a whole number, then 2 and 21,010,076.5 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 42,020,153
-1 -42,020,153

Now, we try dividing 42,020,153 by 3:

42,020,153 ÷ 3 = 14,006,717.6667

If the quotient is a whole number, then 3 and 14,006,717.6667 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 42,020,153
-1 -42,020,153

Let's try dividing by 4:

42,020,153 ÷ 4 = 10,505,038.25

If the quotient is a whole number, then 4 and 10,505,038.25 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 42,020,153
-1 42,020,153
Keep dividing by the next highest number until you cannot divide anymore.

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

17191331931,3511,6373,66711,45925,66931,103217,721315,9412,211,5876,002,87942,020,153
-1-7-19-133-193-1,351-1,637-3,667-11,459-25,669-31,103-217,721-315,941-2,211,587-6,002,879-42,020,153

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