Q: What are the factor combinations of the number 107,456,219?

 A:
Positive:   1 x 10745621913 x 826586373 x 1472003199 x 539981569 x 188851949 x 1132312587 x 415377397 x 14527
Negative: -1 x -107456219-13 x -8265863-73 x -1472003-199 x -539981-569 x -188851-949 x -113231-2587 x -41537-7397 x -14527


How do I find the factor combinations of the number 107,456,219?

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 107,456,219, 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.

1 107,456,219
-1 -107,456,219

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 107,456,219.

Example:
1 x 107,456,219 = 107,456,219
and
-1 x -107,456,219 = 107,456,219
Notice both answers equal 107,456,219

With that explanation out of the way, let's continue. Next, we take the number 107,456,219 and divide it by 2:

107,456,219 ÷ 2 = 53,728,109.5

If the quotient is a whole number, then 2 and 53,728,109.5 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:

1 107,456,219
-1 -107,456,219

Now, we try dividing 107,456,219 by 3:

107,456,219 ÷ 3 = 35,818,739.6667

If the quotient is a whole number, then 3 and 35,818,739.6667 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:

1 107,456,219
-1 -107,456,219

Let's try dividing by 4:

107,456,219 ÷ 4 = 26,864,054.75

If the quotient is a whole number, then 4 and 26,864,054.75 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:

1 107,456,219
-1 107,456,219
Keep dividing by the next highest number until you cannot divide anymore.

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

113731995699492,5877,39714,52741,537113,231188,851539,9811,472,0038,265,863107,456,219
-1-13-73-199-569-949-2,587-7,397-14,527-41,537-113,231-188,851-539,981-1,472,003-8,265,863-107,456,219

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