Q: What are the factor combinations of the number 748,300,105?

 A:
Positive:   1 x 7483001055 x 1496600217 x 10690001535 x 21380003271 x 27612551355 x 5522511897 x 3944659485 x 78893
Negative: -1 x -748300105-5 x -149660021-7 x -106900015-35 x -21380003-271 x -2761255-1355 x -552251-1897 x -394465-9485 x -78893


How do I find the factor combinations of the number 748,300,105?

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 748,300,105, 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.

1 748,300,105
-1 -748,300,105

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 748,300,105.

Example:
1 x 748,300,105 = 748,300,105
and
-1 x -748,300,105 = 748,300,105
Notice both answers equal 748,300,105

With that explanation out of the way, let's continue. Next, we take the number 748,300,105 and divide it by 2:

748,300,105 ÷ 2 = 374,150,052.5

If the quotient is a whole number, then 2 and 374,150,052.5 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:

1 748,300,105
-1 -748,300,105

Now, we try dividing 748,300,105 by 3:

748,300,105 ÷ 3 = 249,433,368.3333

If the quotient is a whole number, then 3 and 249,433,368.3333 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:

1 748,300,105
-1 -748,300,105

Let's try dividing by 4:

748,300,105 ÷ 4 = 187,075,026.25

If the quotient is a whole number, then 4 and 187,075,026.25 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:

1 748,300,105
-1 748,300,105
Keep dividing by the next highest number until you cannot divide anymore.

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

157352711,3551,8979,48578,893394,465552,2512,761,25521,380,003106,900,015149,660,021748,300,105
-1-5-7-35-271-1,355-1,897-9,485-78,893-394,465-552,251-2,761,255-21,380,003-106,900,015-149,660,021-748,300,105

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