Q: What are the factor combinations of the number 105,498,745?

 A:
Positive:   1 x 1054987455 x 2109974911 x 959079555 x 1918159389 x 2712051945 x 542414279 x 246554931 x 21395
Negative: -1 x -105498745-5 x -21099749-11 x -9590795-55 x -1918159-389 x -271205-1945 x -54241-4279 x -24655-4931 x -21395


How do I find the factor combinations of the number 105,498,745?

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 105,498,745, 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.

1 105,498,745
-1 -105,498,745

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 105,498,745.

Example:
1 x 105,498,745 = 105,498,745
and
-1 x -105,498,745 = 105,498,745
Notice both answers equal 105,498,745

With that explanation out of the way, let's continue. Next, we take the number 105,498,745 and divide it by 2:

105,498,745 ÷ 2 = 52,749,372.5

If the quotient is a whole number, then 2 and 52,749,372.5 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:

1 105,498,745
-1 -105,498,745

Now, we try dividing 105,498,745 by 3:

105,498,745 ÷ 3 = 35,166,248.3333

If the quotient is a whole number, then 3 and 35,166,248.3333 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:

1 105,498,745
-1 -105,498,745

Let's try dividing by 4:

105,498,745 ÷ 4 = 26,374,686.25

If the quotient is a whole number, then 4 and 26,374,686.25 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:

1 105,498,745
-1 105,498,745
Keep dividing by the next highest number until you cannot divide anymore.

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

1511553891,9454,2794,93121,39524,65554,241271,2051,918,1599,590,79521,099,749105,498,745
-1-5-11-55-389-1,945-4,279-4,931-21,395-24,655-54,241-271,205-1,918,159-9,590,795-21,099,749-105,498,745

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