Q: What are the factor combinations of the number 38,605?

 A:
Positive:   1 x 386055 x 77217 x 551535 x 1103
Negative: -1 x -38605-5 x -7721-7 x -5515-35 x -1103


How do I find the factor combinations of the number 38,605?

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 38,605, 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 38,605
-1 -38,605

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 38,605.

Example:
1 x 38,605 = 38,605
and
-1 x -38,605 = 38,605
Notice both answers equal 38,605

With that explanation out of the way, let's continue. Next, we take the number 38,605 and divide it by 2:

38,605 ÷ 2 = 19,302.5

If the quotient is a whole number, then 2 and 19,302.5 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 38,605
-1 -38,605

Now, we try dividing 38,605 by 3:

38,605 ÷ 3 = 12,868.3333

If the quotient is a whole number, then 3 and 12,868.3333 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 38,605
-1 -38,605

Let's try dividing by 4:

38,605 ÷ 4 = 9,651.25

If the quotient is a whole number, then 4 and 9,651.25 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 38,605
-1 38,605
Keep dividing by the next highest number until you cannot divide anymore.

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

157351,1035,5157,72138,605
-1-5-7-35-1,103-5,515-7,721-38,605

More Examples

Here are some more numbers to try:

Try the factor calculator

Explore more about the number 38,605:


Ask a Question