Q: What are the factor combinations of the number 213,636,527?

 A:
Positive:   1 x 21363652713 x 1643357941 x 5210647277 x 771251533 x 4008191447 x 1476413601 x 5932711357 x 18811
Negative: -1 x -213636527-13 x -16433579-41 x -5210647-277 x -771251-533 x -400819-1447 x -147641-3601 x -59327-11357 x -18811


How do I find the factor combinations of the number 213,636,527?

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 213,636,527, 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.

1 213,636,527
-1 -213,636,527

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 213,636,527.

Example:
1 x 213,636,527 = 213,636,527
and
-1 x -213,636,527 = 213,636,527
Notice both answers equal 213,636,527

With that explanation out of the way, let's continue. Next, we take the number 213,636,527 and divide it by 2:

213,636,527 ÷ 2 = 106,818,263.5

If the quotient is a whole number, then 2 and 106,818,263.5 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:

1 213,636,527
-1 -213,636,527

Now, we try dividing 213,636,527 by 3:

213,636,527 ÷ 3 = 71,212,175.6667

If the quotient is a whole number, then 3 and 71,212,175.6667 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:

1 213,636,527
-1 -213,636,527

Let's try dividing by 4:

213,636,527 ÷ 4 = 53,409,131.75

If the quotient is a whole number, then 4 and 53,409,131.75 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:

1 213,636,527
-1 213,636,527
Keep dividing by the next highest number until you cannot divide anymore.

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

113412775331,4473,60111,35718,81159,327147,641400,819771,2515,210,64716,433,579213,636,527
-1-13-41-277-533-1,447-3,601-11,357-18,811-59,327-147,641-400,819-771,251-5,210,647-16,433,579-213,636,527

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