Q: What are the factor combinations of the number 210,524,045?

 A:
Positive:   1 x 2105240455 x 4210480947 x 4479235235 x 895847367 x 5736351835 x 1147272441 x 8624512205 x 17249
Negative: -1 x -210524045-5 x -42104809-47 x -4479235-235 x -895847-367 x -573635-1835 x -114727-2441 x -86245-12205 x -17249


How do I find the factor combinations of the number 210,524,045?

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 210,524,045, 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.

1 210,524,045
-1 -210,524,045

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 210,524,045.

Example:
1 x 210,524,045 = 210,524,045
and
-1 x -210,524,045 = 210,524,045
Notice both answers equal 210,524,045

With that explanation out of the way, let's continue. Next, we take the number 210,524,045 and divide it by 2:

210,524,045 ÷ 2 = 105,262,022.5

If the quotient is a whole number, then 2 and 105,262,022.5 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:

1 210,524,045
-1 -210,524,045

Now, we try dividing 210,524,045 by 3:

210,524,045 ÷ 3 = 70,174,681.6667

If the quotient is a whole number, then 3 and 70,174,681.6667 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:

1 210,524,045
-1 -210,524,045

Let's try dividing by 4:

210,524,045 ÷ 4 = 52,631,011.25

If the quotient is a whole number, then 4 and 52,631,011.25 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:

1 210,524,045
-1 210,524,045
Keep dividing by the next highest number until you cannot divide anymore.

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

15472353671,8352,44112,20517,24986,245114,727573,635895,8474,479,23542,104,809210,524,045
-1-5-47-235-367-1,835-2,441-12,205-17,249-86,245-114,727-573,635-895,847-4,479,235-42,104,809-210,524,045

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