Q: What are the factor combinations of the number 172,352,069?

 A:
Positive:   1 x 17235206917 x 1013835741 x 4203709107 x 1610767697 x 2472771819 x 947512311 x 745794387 x 39287
Negative: -1 x -172352069-17 x -10138357-41 x -4203709-107 x -1610767-697 x -247277-1819 x -94751-2311 x -74579-4387 x -39287


How do I find the factor combinations of the number 172,352,069?

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 172,352,069, 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.

1 172,352,069
-1 -172,352,069

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 172,352,069.

Example:
1 x 172,352,069 = 172,352,069
and
-1 x -172,352,069 = 172,352,069
Notice both answers equal 172,352,069

With that explanation out of the way, let's continue. Next, we take the number 172,352,069 and divide it by 2:

172,352,069 ÷ 2 = 86,176,034.5

If the quotient is a whole number, then 2 and 86,176,034.5 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:

1 172,352,069
-1 -172,352,069

Now, we try dividing 172,352,069 by 3:

172,352,069 ÷ 3 = 57,450,689.6667

If the quotient is a whole number, then 3 and 57,450,689.6667 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:

1 172,352,069
-1 -172,352,069

Let's try dividing by 4:

172,352,069 ÷ 4 = 43,088,017.25

If the quotient is a whole number, then 4 and 43,088,017.25 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:

1 172,352,069
-1 172,352,069
Keep dividing by the next highest number until you cannot divide anymore.

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

117411076971,8192,3114,38739,28774,57994,751247,2771,610,7674,203,70910,138,357172,352,069
-1-17-41-107-697-1,819-2,311-4,387-39,287-74,579-94,751-247,277-1,610,767-4,203,709-10,138,357-172,352,069

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