Q: What are the factor combinations of the number 214,775?

 A:
Positive:   1 x 2147755 x 4295511 x 1952525 x 859155 x 390571 x 3025121 x 1775275 x 781355 x 605
Negative: -1 x -214775-5 x -42955-11 x -19525-25 x -8591-55 x -3905-71 x -3025-121 x -1775-275 x -781-355 x -605


How do I find the factor combinations of the number 214,775?

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 214,775, 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.

1 214,775
-1 -214,775

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 214,775.

Example:
1 x 214,775 = 214,775
and
-1 x -214,775 = 214,775
Notice both answers equal 214,775

With that explanation out of the way, let's continue. Next, we take the number 214,775 and divide it by 2:

214,775 ÷ 2 = 107,387.5

If the quotient is a whole number, then 2 and 107,387.5 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:

1 214,775
-1 -214,775

Now, we try dividing 214,775 by 3:

214,775 ÷ 3 = 71,591.6667

If the quotient is a whole number, then 3 and 71,591.6667 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:

1 214,775
-1 -214,775

Let's try dividing by 4:

214,775 ÷ 4 = 53,693.75

If the quotient is a whole number, then 4 and 53,693.75 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:

1 214,775
-1 214,775
Keep dividing by the next highest number until you cannot divide anymore.

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

15112555711212753556057811,7753,0253,9058,59119,52542,955214,775
-1-5-11-25-55-71-121-275-355-605-781-1,775-3,025-3,905-8,591-19,525-42,955-214,775

More Examples

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