Q: What are the factor combinations of the number 211,171?

 A:
Positive:   1 x 21117147 x 4493
Negative: -1 x -211171-47 x -4493


How do I find the factor combinations of the number 211,171?

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 211,171, 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.

1 211,171
-1 -211,171

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 211,171.

Example:
1 x 211,171 = 211,171
and
-1 x -211,171 = 211,171
Notice both answers equal 211,171

With that explanation out of the way, let's continue. Next, we take the number 211,171 and divide it by 2:

211,171 ÷ 2 = 105,585.5

If the quotient is a whole number, then 2 and 105,585.5 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:

1 211,171
-1 -211,171

Now, we try dividing 211,171 by 3:

211,171 ÷ 3 = 70,390.3333

If the quotient is a whole number, then 3 and 70,390.3333 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:

1 211,171
-1 -211,171

Let's try dividing by 4:

211,171 ÷ 4 = 52,792.75

If the quotient is a whole number, then 4 and 52,792.75 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:

1 211,171
-1 211,171
Keep dividing by the next highest number until you cannot divide anymore.

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

1474,493211,171
-1-47-4,493-211,171

More Examples

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