Q: What are the factor combinations of the number 4,202,303?

 A:
Positive:   1 x 42023037 x 60032929 x 144907127 x 33089163 x 25781203 x 20701889 x 47271141 x 3683
Negative: -1 x -4202303-7 x -600329-29 x -144907-127 x -33089-163 x -25781-203 x -20701-889 x -4727-1141 x -3683


How do I find the factor combinations of the number 4,202,303?

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 4,202,303, 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 4,202,303
-1 -4,202,303

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 4,202,303.

Example:
1 x 4,202,303 = 4,202,303
and
-1 x -4,202,303 = 4,202,303
Notice both answers equal 4,202,303

With that explanation out of the way, let's continue. Next, we take the number 4,202,303 and divide it by 2:

4,202,303 ÷ 2 = 2,101,151.5

If the quotient is a whole number, then 2 and 2,101,151.5 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 4,202,303
-1 -4,202,303

Now, we try dividing 4,202,303 by 3:

4,202,303 ÷ 3 = 1,400,767.6667

If the quotient is a whole number, then 3 and 1,400,767.6667 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 4,202,303
-1 -4,202,303

Let's try dividing by 4:

4,202,303 ÷ 4 = 1,050,575.75

If the quotient is a whole number, then 4 and 1,050,575.75 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 4,202,303
-1 4,202,303
Keep dividing by the next highest number until you cannot divide anymore.

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

17291271632038891,1413,6834,72720,70125,78133,089144,907600,3294,202,303
-1-7-29-127-163-203-889-1,141-3,683-4,727-20,701-25,781-33,089-144,907-600,329-4,202,303

More Examples

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