Q: What are the factor combinations of the number 46,223?

 A:
Positive:   1 x 4622317 x 2719
Negative: -1 x -46223-17 x -2719


How do I find the factor combinations of the number 46,223?

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 46,223, 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 46,223
-1 -46,223

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 46,223.

Example:
1 x 46,223 = 46,223
and
-1 x -46,223 = 46,223
Notice both answers equal 46,223

With that explanation out of the way, let's continue. Next, we take the number 46,223 and divide it by 2:

46,223 ÷ 2 = 23,111.5

If the quotient is a whole number, then 2 and 23,111.5 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 46,223
-1 -46,223

Now, we try dividing 46,223 by 3:

46,223 ÷ 3 = 15,407.6667

If the quotient is a whole number, then 3 and 15,407.6667 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 46,223
-1 -46,223

Let's try dividing by 4:

46,223 ÷ 4 = 11,555.75

If the quotient is a whole number, then 4 and 11,555.75 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 46,223
-1 46,223
Keep dividing by the next highest number until you cannot divide anymore.

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

1172,71946,223
-1-17-2,719-46,223

More Examples

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