Q: What are the factor combinations of the number 106,421?

 A:
Positive:   1 x 1064217 x 1520323 x 4627161 x 661
Negative: -1 x -106421-7 x -15203-23 x -4627-161 x -661


How do I find the factor combinations of the number 106,421?

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 106,421, 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.

1 106,421
-1 -106,421

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 106,421.

Example:
1 x 106,421 = 106,421
and
-1 x -106,421 = 106,421
Notice both answers equal 106,421

With that explanation out of the way, let's continue. Next, we take the number 106,421 and divide it by 2:

106,421 ÷ 2 = 53,210.5

If the quotient is a whole number, then 2 and 53,210.5 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:

1 106,421
-1 -106,421

Now, we try dividing 106,421 by 3:

106,421 ÷ 3 = 35,473.6667

If the quotient is a whole number, then 3 and 35,473.6667 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:

1 106,421
-1 -106,421

Let's try dividing by 4:

106,421 ÷ 4 = 26,605.25

If the quotient is a whole number, then 4 and 26,605.25 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:

1 106,421
-1 106,421
Keep dividing by the next highest number until you cannot divide anymore.

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

17231616614,62715,203106,421
-1-7-23-161-661-4,627-15,203-106,421

More Examples

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