Q: What are the factor combinations of the number 838,145?

 A:
Positive:   1 x 8381455 x 1676297 x 11973511 x 7619535 x 2394749 x 1710555 x 1523977 x 10885245 x 3421311 x 2695385 x 2177539 x 1555
Negative: -1 x -838145-5 x -167629-7 x -119735-11 x -76195-35 x -23947-49 x -17105-55 x -15239-77 x -10885-245 x -3421-311 x -2695-385 x -2177-539 x -1555


How do I find the factor combinations of the number 838,145?

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 838,145, 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.

1 838,145
-1 -838,145

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 838,145.

Example:
1 x 838,145 = 838,145
and
-1 x -838,145 = 838,145
Notice both answers equal 838,145

With that explanation out of the way, let's continue. Next, we take the number 838,145 and divide it by 2:

838,145 ÷ 2 = 419,072.5

If the quotient is a whole number, then 2 and 419,072.5 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:

1 838,145
-1 -838,145

Now, we try dividing 838,145 by 3:

838,145 ÷ 3 = 279,381.6667

If the quotient is a whole number, then 3 and 279,381.6667 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:

1 838,145
-1 -838,145

Let's try dividing by 4:

838,145 ÷ 4 = 209,536.25

If the quotient is a whole number, then 4 and 209,536.25 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:

1 838,145
-1 838,145
Keep dividing by the next highest number until you cannot divide anymore.

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

15711354955772453113855391,5552,1772,6953,42110,88515,23917,10523,94776,195119,735167,629838,145
-1-5-7-11-35-49-55-77-245-311-385-539-1,555-2,177-2,695-3,421-10,885-15,239-17,105-23,947-76,195-119,735-167,629-838,145

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