Q: What are the factor combinations of the number 210,421,135?

 A:
Positive:   1 x 2104211355 x 4208422723 x 9148745115 x 1829749233 x 9030951165 x 1806195359 x 392657853 x 26795
Negative: -1 x -210421135-5 x -42084227-23 x -9148745-115 x -1829749-233 x -903095-1165 x -180619-5359 x -39265-7853 x -26795


How do I find the factor combinations of the number 210,421,135?

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 210,421,135, 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.

1 210,421,135
-1 -210,421,135

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 210,421,135.

Example:
1 x 210,421,135 = 210,421,135
and
-1 x -210,421,135 = 210,421,135
Notice both answers equal 210,421,135

With that explanation out of the way, let's continue. Next, we take the number 210,421,135 and divide it by 2:

210,421,135 ÷ 2 = 105,210,567.5

If the quotient is a whole number, then 2 and 105,210,567.5 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:

1 210,421,135
-1 -210,421,135

Now, we try dividing 210,421,135 by 3:

210,421,135 ÷ 3 = 70,140,378.3333

If the quotient is a whole number, then 3 and 70,140,378.3333 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:

1 210,421,135
-1 -210,421,135

Let's try dividing by 4:

210,421,135 ÷ 4 = 52,605,283.75

If the quotient is a whole number, then 4 and 52,605,283.75 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:

1 210,421,135
-1 210,421,135
Keep dividing by the next highest number until you cannot divide anymore.

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

15231152331,1655,3597,85326,79539,265180,619903,0951,829,7499,148,74542,084,227210,421,135
-1-5-23-115-233-1,165-5,359-7,853-26,795-39,265-180,619-903,095-1,829,749-9,148,745-42,084,227-210,421,135

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