Q: What are the factor combinations of the number 210,535,423?

 A:
Positive:   1 x 2105354237 x 3007648959 x 3568397413 x 509771709 x 296947719 x 2928174963 x 424215033 x 41831
Negative: -1 x -210535423-7 x -30076489-59 x -3568397-413 x -509771-709 x -296947-719 x -292817-4963 x -42421-5033 x -41831


How do I find the factor combinations of the number 210,535,423?

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 210,535,423, 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.

1 210,535,423
-1 -210,535,423

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 210,535,423.

Example:
1 x 210,535,423 = 210,535,423
and
-1 x -210,535,423 = 210,535,423
Notice both answers equal 210,535,423

With that explanation out of the way, let's continue. Next, we take the number 210,535,423 and divide it by 2:

210,535,423 ÷ 2 = 105,267,711.5

If the quotient is a whole number, then 2 and 105,267,711.5 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:

1 210,535,423
-1 -210,535,423

Now, we try dividing 210,535,423 by 3:

210,535,423 ÷ 3 = 70,178,474.3333

If the quotient is a whole number, then 3 and 70,178,474.3333 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:

1 210,535,423
-1 -210,535,423

Let's try dividing by 4:

210,535,423 ÷ 4 = 52,633,855.75

If the quotient is a whole number, then 4 and 52,633,855.75 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:

1 210,535,423
-1 210,535,423
Keep dividing by the next highest number until you cannot divide anymore.

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

17594137097194,9635,03341,83142,421292,817296,947509,7713,568,39730,076,489210,535,423
-1-7-59-413-709-719-4,963-5,033-41,831-42,421-292,817-296,947-509,771-3,568,397-30,076,489-210,535,423

More Examples

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