Q: What are the factor combinations of the number 828,971?

 A:
Positive:   1 x 82897111 x 7536113 x 6376717 x 4876331 x 26741121 x 6851143 x 5797187 x 4433221 x 3751341 x 2431403 x 2057527 x 1573
Negative: -1 x -828971-11 x -75361-13 x -63767-17 x -48763-31 x -26741-121 x -6851-143 x -5797-187 x -4433-221 x -3751-341 x -2431-403 x -2057-527 x -1573


How do I find the factor combinations of the number 828,971?

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 828,971, 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.

1 828,971
-1 -828,971

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 828,971.

Example:
1 x 828,971 = 828,971
and
-1 x -828,971 = 828,971
Notice both answers equal 828,971

With that explanation out of the way, let's continue. Next, we take the number 828,971 and divide it by 2:

828,971 ÷ 2 = 414,485.5

If the quotient is a whole number, then 2 and 414,485.5 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:

1 828,971
-1 -828,971

Now, we try dividing 828,971 by 3:

828,971 ÷ 3 = 276,323.6667

If the quotient is a whole number, then 3 and 276,323.6667 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:

1 828,971
-1 -828,971

Let's try dividing by 4:

828,971 ÷ 4 = 207,242.75

If the quotient is a whole number, then 4 and 207,242.75 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:

1 828,971
-1 828,971
Keep dividing by the next highest number until you cannot divide anymore.

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

1111317311211431872213414035271,5732,0572,4313,7514,4335,7976,85126,74148,76363,76775,361828,971
-1-11-13-17-31-121-143-187-221-341-403-527-1,573-2,057-2,431-3,751-4,433-5,797-6,851-26,741-48,763-63,767-75,361-828,971

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