Q: What are the factor combinations of the number 42,005,105?

 A:
Positive:   1 x 420051055 x 840102119 x 221079595 x 442159139 x 302195695 x 604392641 x 159053181 x 13205
Negative: -1 x -42005105-5 x -8401021-19 x -2210795-95 x -442159-139 x -302195-695 x -60439-2641 x -15905-3181 x -13205


How do I find the factor combinations of the number 42,005,105?

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 42,005,105, 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 42,005,105
-1 -42,005,105

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 42,005,105.

Example:
1 x 42,005,105 = 42,005,105
and
-1 x -42,005,105 = 42,005,105
Notice both answers equal 42,005,105

With that explanation out of the way, let's continue. Next, we take the number 42,005,105 and divide it by 2:

42,005,105 ÷ 2 = 21,002,552.5

If the quotient is a whole number, then 2 and 21,002,552.5 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 42,005,105
-1 -42,005,105

Now, we try dividing 42,005,105 by 3:

42,005,105 ÷ 3 = 14,001,701.6667

If the quotient is a whole number, then 3 and 14,001,701.6667 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 42,005,105
-1 -42,005,105

Let's try dividing by 4:

42,005,105 ÷ 4 = 10,501,276.25

If the quotient is a whole number, then 4 and 10,501,276.25 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 42,005,105
-1 42,005,105
Keep dividing by the next highest number until you cannot divide anymore.

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

1519951396952,6413,18113,20515,90560,439302,195442,1592,210,7958,401,02142,005,105
-1-5-19-95-139-695-2,641-3,181-13,205-15,905-60,439-302,195-442,159-2,210,795-8,401,021-42,005,105

More Examples

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