Q: What are the factor combinations of the number 4,200,215?

 A:
Positive:   1 x 42002155 x 84004329 x 14483583 x 50605145 x 28967349 x 12035415 x 101211745 x 2407
Negative: -1 x -4200215-5 x -840043-29 x -144835-83 x -50605-145 x -28967-349 x -12035-415 x -10121-1745 x -2407


How do I find the factor combinations of the number 4,200,215?

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 4,200,215, 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 4,200,215
-1 -4,200,215

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 4,200,215.

Example:
1 x 4,200,215 = 4,200,215
and
-1 x -4,200,215 = 4,200,215
Notice both answers equal 4,200,215

With that explanation out of the way, let's continue. Next, we take the number 4,200,215 and divide it by 2:

4,200,215 ÷ 2 = 2,100,107.5

If the quotient is a whole number, then 2 and 2,100,107.5 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 4,200,215
-1 -4,200,215

Now, we try dividing 4,200,215 by 3:

4,200,215 ÷ 3 = 1,400,071.6667

If the quotient is a whole number, then 3 and 1,400,071.6667 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 4,200,215
-1 -4,200,215

Let's try dividing by 4:

4,200,215 ÷ 4 = 1,050,053.75

If the quotient is a whole number, then 4 and 1,050,053.75 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 4,200,215
-1 4,200,215
Keep dividing by the next highest number until you cannot divide anymore.

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

1529831453494151,7452,40710,12112,03528,96750,605144,835840,0434,200,215
-1-5-29-83-145-349-415-1,745-2,407-10,121-12,035-28,967-50,605-144,835-840,043-4,200,215

More Examples

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