Q: What are the factor combinations of the number 210,242,621?

 A:
Positive:   1 x 21024262117 x 1236721337 x 568223379 x 2661299629 x 3342491343 x 1565472923 x 719274231 x 49691
Negative: -1 x -210242621-17 x -12367213-37 x -5682233-79 x -2661299-629 x -334249-1343 x -156547-2923 x -71927-4231 x -49691


How do I find the factor combinations of the number 210,242,621?

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 210,242,621, 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.

1 210,242,621
-1 -210,242,621

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 210,242,621.

Example:
1 x 210,242,621 = 210,242,621
and
-1 x -210,242,621 = 210,242,621
Notice both answers equal 210,242,621

With that explanation out of the way, let's continue. Next, we take the number 210,242,621 and divide it by 2:

210,242,621 ÷ 2 = 105,121,310.5

If the quotient is a whole number, then 2 and 105,121,310.5 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:

1 210,242,621
-1 -210,242,621

Now, we try dividing 210,242,621 by 3:

210,242,621 ÷ 3 = 70,080,873.6667

If the quotient is a whole number, then 3 and 70,080,873.6667 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:

1 210,242,621
-1 -210,242,621

Let's try dividing by 4:

210,242,621 ÷ 4 = 52,560,655.25

If the quotient is a whole number, then 4 and 52,560,655.25 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:

1 210,242,621
-1 210,242,621
Keep dividing by the next highest number until you cannot divide anymore.

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

11737796291,3432,9234,23149,69171,927156,547334,2492,661,2995,682,23312,367,213210,242,621
-1-17-37-79-629-1,343-2,923-4,231-49,691-71,927-156,547-334,249-2,661,299-5,682,233-12,367,213-210,242,621

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