Q: What are the factor combinations of the number 104,365,145?

 A:
Positive:   1 x 1043651455 x 2087302923 x 453761547 x 2220535115 x 907523235 x 4441071081 x 965455405 x 19309
Negative: -1 x -104365145-5 x -20873029-23 x -4537615-47 x -2220535-115 x -907523-235 x -444107-1081 x -96545-5405 x -19309


How do I find the factor combinations of the number 104,365,145?

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 104,365,145, 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.

1 104,365,145
-1 -104,365,145

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 104,365,145.

Example:
1 x 104,365,145 = 104,365,145
and
-1 x -104,365,145 = 104,365,145
Notice both answers equal 104,365,145

With that explanation out of the way, let's continue. Next, we take the number 104,365,145 and divide it by 2:

104,365,145 ÷ 2 = 52,182,572.5

If the quotient is a whole number, then 2 and 52,182,572.5 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:

1 104,365,145
-1 -104,365,145

Now, we try dividing 104,365,145 by 3:

104,365,145 ÷ 3 = 34,788,381.6667

If the quotient is a whole number, then 3 and 34,788,381.6667 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:

1 104,365,145
-1 -104,365,145

Let's try dividing by 4:

104,365,145 ÷ 4 = 26,091,286.25

If the quotient is a whole number, then 4 and 26,091,286.25 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:

1 104,365,145
-1 104,365,145
Keep dividing by the next highest number until you cannot divide anymore.

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

1523471152351,0815,40519,30996,545444,107907,5232,220,5354,537,61520,873,029104,365,145
-1-5-23-47-115-235-1,081-5,405-19,309-96,545-444,107-907,523-2,220,535-4,537,615-20,873,029-104,365,145

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