Q: What are the factor combinations of the number 445?

 A:
Positive:   1 x 4455 x 89
Negative: -1 x -445-5 x -89


How do I find the factor combinations of the number 445?

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 445, 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.

1 445
-1 -445

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 445.

Example:
1 x 445 = 445
and
-1 x -445 = 445
Notice both answers equal 445

With that explanation out of the way, let's continue. Next, we take the number 445 and divide it by 2:

445 ÷ 2 = 222.5

If the quotient is a whole number, then 2 and 222.5 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:

1 445
-1 -445

Now, we try dividing 445 by 3:

445 ÷ 3 = 148.3333

If the quotient is a whole number, then 3 and 148.3333 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:

1 445
-1 -445

Let's try dividing by 4:

445 ÷ 4 = 111.25

If the quotient is a whole number, then 4 and 111.25 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:

1 445
-1 445
Keep dividing by the next highest number until you cannot divide anymore.

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

1589445
-1-5-89-445

More Examples

Here are some more numbers to try:

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