Q: What are the factor combinations of the number 45,042,209?

 A:
Positive:   1 x 4504220937 x 121735753 x 849853103 x 437303223 x 2019831961 x 229693811 x 118195459 x 8251
Negative: -1 x -45042209-37 x -1217357-53 x -849853-103 x -437303-223 x -201983-1961 x -22969-3811 x -11819-5459 x -8251


How do I find the factor combinations of the number 45,042,209?

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 45,042,209, 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 45,042,209
-1 -45,042,209

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 45,042,209.

Example:
1 x 45,042,209 = 45,042,209
and
-1 x -45,042,209 = 45,042,209
Notice both answers equal 45,042,209

With that explanation out of the way, let's continue. Next, we take the number 45,042,209 and divide it by 2:

45,042,209 ÷ 2 = 22,521,104.5

If the quotient is a whole number, then 2 and 22,521,104.5 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 45,042,209
-1 -45,042,209

Now, we try dividing 45,042,209 by 3:

45,042,209 ÷ 3 = 15,014,069.6667

If the quotient is a whole number, then 3 and 15,014,069.6667 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 45,042,209
-1 -45,042,209

Let's try dividing by 4:

45,042,209 ÷ 4 = 11,260,552.25

If the quotient is a whole number, then 4 and 11,260,552.25 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 45,042,209
-1 45,042,209
Keep dividing by the next highest number until you cannot divide anymore.

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

137531032231,9613,8115,4598,25111,81922,969201,983437,303849,8531,217,35745,042,209
-1-37-53-103-223-1,961-3,811-5,459-8,251-11,819-22,969-201,983-437,303-849,853-1,217,357-45,042,209

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