Q: What are the factor combinations of the number 42,168,019?

 A:
Positive:   1 x 4216801953 x 79562361 x 6912793233 x 13043
Negative: -1 x -42168019-53 x -795623-61 x -691279-3233 x -13043


How do I find the factor combinations of the number 42,168,019?

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 42,168,019, 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 42,168,019
-1 -42,168,019

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 42,168,019.

Example:
1 x 42,168,019 = 42,168,019
and
-1 x -42,168,019 = 42,168,019
Notice both answers equal 42,168,019

With that explanation out of the way, let's continue. Next, we take the number 42,168,019 and divide it by 2:

42,168,019 ÷ 2 = 21,084,009.5

If the quotient is a whole number, then 2 and 21,084,009.5 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 42,168,019
-1 -42,168,019

Now, we try dividing 42,168,019 by 3:

42,168,019 ÷ 3 = 14,056,006.3333

If the quotient is a whole number, then 3 and 14,056,006.3333 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 42,168,019
-1 -42,168,019

Let's try dividing by 4:

42,168,019 ÷ 4 = 10,542,004.75

If the quotient is a whole number, then 4 and 10,542,004.75 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 42,168,019
-1 42,168,019
Keep dividing by the next highest number until you cannot divide anymore.

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

153613,23313,043691,279795,62342,168,019
-1-53-61-3,233-13,043-691,279-795,623-42,168,019

More Examples

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