Q: What are the factor combinations of the number 42,003,205?

 A:
Positive:   1 x 420032055 x 840064119 x 221069595 x 442139
Negative: -1 x -42003205-5 x -8400641-19 x -2210695-95 x -442139


How do I find the factor combinations of the number 42,003,205?

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 42,003,205, 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 42,003,205
-1 -42,003,205

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 42,003,205.

Example:
1 x 42,003,205 = 42,003,205
and
-1 x -42,003,205 = 42,003,205
Notice both answers equal 42,003,205

With that explanation out of the way, let's continue. Next, we take the number 42,003,205 and divide it by 2:

42,003,205 ÷ 2 = 21,001,602.5

If the quotient is a whole number, then 2 and 21,001,602.5 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 42,003,205
-1 -42,003,205

Now, we try dividing 42,003,205 by 3:

42,003,205 ÷ 3 = 14,001,068.3333

If the quotient is a whole number, then 3 and 14,001,068.3333 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 42,003,205
-1 -42,003,205

Let's try dividing by 4:

42,003,205 ÷ 4 = 10,500,801.25

If the quotient is a whole number, then 4 and 10,500,801.25 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 42,003,205
-1 42,003,205
Keep dividing by the next highest number until you cannot divide anymore.

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

151995442,1392,210,6958,400,64142,003,205
-1-5-19-95-442,139-2,210,695-8,400,641-42,003,205

More Examples

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