Q: What are the factor combinations of the number 135,108?

 A:
Positive:   1 x 1351082 x 675543 x 450364 x 337776 x 225189 x 1501212 x 1125918 x 750627 x 500436 x 375354 x 250281 x 1668108 x 1251139 x 972162 x 834243 x 556278 x 486324 x 417
Negative: -1 x -135108-2 x -67554-3 x -45036-4 x -33777-6 x -22518-9 x -15012-12 x -11259-18 x -7506-27 x -5004-36 x -3753-54 x -2502-81 x -1668-108 x -1251-139 x -972-162 x -834-243 x -556-278 x -486-324 x -417


How do I find the factor combinations of the number 135,108?

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 135,108, 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.

1 135,108
-1 -135,108

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 135,108.

Example:
1 x 135,108 = 135,108
and
-1 x -135,108 = 135,108
Notice both answers equal 135,108

With that explanation out of the way, let's continue. Next, we take the number 135,108 and divide it by 2:

135,108 ÷ 2 = 67,554

If the quotient is a whole number, then 2 and 67,554 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 67,554 135,108
-1 -2 -67,554 -135,108

Now, we try dividing 135,108 by 3:

135,108 ÷ 3 = 45,036

If the quotient is a whole number, then 3 and 45,036 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 45,036 67,554 135,108
-1 -2 -3 -45,036 -67,554 -135,108

Let's try dividing by 4:

135,108 ÷ 4 = 33,777

If the quotient is a whole number, then 4 and 33,777 are factors. In this case, the quotient is a whole number. Write them in the table inside the other two factors like the below example. Don't forget to write the negative numbers too!

Here is what our table should look like at this step:

1 2 3 4 33,777 45,036 67,554 135,108
-1 -2 -3 -4 -33,777 -45,036 -67,554 135,108
Keep dividing by the next highest number until you cannot divide anymore.

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

1234691218273654811081391622432783244174865568349721,2511,6682,5023,7535,0047,50611,25915,01222,51833,77745,03667,554135,108
-1-2-3-4-6-9-12-18-27-36-54-81-108-139-162-243-278-324-417-486-556-834-972-1,251-1,668-2,502-3,753-5,004-7,506-11,259-15,012-22,518-33,777-45,036-67,554-135,108

More Examples

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