Q: What are the factor combinations of the number 17,606,729?

 A:
Positive:   1 x 176067297 x 251524731 x 56795949 x 35932167 x 262787173 x 101773217 x 81137469 x 375411211 x 145391519 x 115912077 x 84773283 x 5363
Negative: -1 x -17606729-7 x -2515247-31 x -567959-49 x -359321-67 x -262787-173 x -101773-217 x -81137-469 x -37541-1211 x -14539-1519 x -11591-2077 x -8477-3283 x -5363


How do I find the factor combinations of the number 17,606,729?

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 17,606,729, 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 17,606,729
-1 -17,606,729

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 17,606,729.

Example:
1 x 17,606,729 = 17,606,729
and
-1 x -17,606,729 = 17,606,729
Notice both answers equal 17,606,729

With that explanation out of the way, let's continue. Next, we take the number 17,606,729 and divide it by 2:

17,606,729 ÷ 2 = 8,803,364.5

If the quotient is a whole number, then 2 and 8,803,364.5 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 17,606,729
-1 -17,606,729

Now, we try dividing 17,606,729 by 3:

17,606,729 ÷ 3 = 5,868,909.6667

If the quotient is a whole number, then 3 and 5,868,909.6667 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 17,606,729
-1 -17,606,729

Let's try dividing by 4:

17,606,729 ÷ 4 = 4,401,682.25

If the quotient is a whole number, then 4 and 4,401,682.25 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 17,606,729
-1 17,606,729
Keep dividing by the next highest number until you cannot divide anymore.

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

173149671732174691,2111,5192,0773,2835,3638,47711,59114,53937,54181,137101,773262,787359,321567,9592,515,24717,606,729
-1-7-31-49-67-173-217-469-1,211-1,519-2,077-3,283-5,363-8,477-11,591-14,539-37,541-81,137-101,773-262,787-359,321-567,959-2,515,247-17,606,729

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