Q: What are the factor combinations of the number 34,222,013?

 A:
Positive:   1 x 342220137 x 488885989 x 384517163 x 209951337 x 101549623 x 549311141 x 299932359 x 14507
Negative: -1 x -34222013-7 x -4888859-89 x -384517-163 x -209951-337 x -101549-623 x -54931-1141 x -29993-2359 x -14507


How do I find the factor combinations of the number 34,222,013?

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 34,222,013, 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 34,222,013
-1 -34,222,013

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 34,222,013.

Example:
1 x 34,222,013 = 34,222,013
and
-1 x -34,222,013 = 34,222,013
Notice both answers equal 34,222,013

With that explanation out of the way, let's continue. Next, we take the number 34,222,013 and divide it by 2:

34,222,013 ÷ 2 = 17,111,006.5

If the quotient is a whole number, then 2 and 17,111,006.5 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 34,222,013
-1 -34,222,013

Now, we try dividing 34,222,013 by 3:

34,222,013 ÷ 3 = 11,407,337.6667

If the quotient is a whole number, then 3 and 11,407,337.6667 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 34,222,013
-1 -34,222,013

Let's try dividing by 4:

34,222,013 ÷ 4 = 8,555,503.25

If the quotient is a whole number, then 4 and 8,555,503.25 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 34,222,013
-1 34,222,013
Keep dividing by the next highest number until you cannot divide anymore.

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

17891633376231,1412,35914,50729,99354,931101,549209,951384,5174,888,85934,222,013
-1-7-89-163-337-623-1,141-2,359-14,507-29,993-54,931-101,549-209,951-384,517-4,888,859-34,222,013

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