Q: What are the factor combinations of the number 301,020?

 A:
Positive:   1 x 3010202 x 1505103 x 1003404 x 752555 x 602046 x 5017010 x 3010212 x 2508515 x 2006820 x 1505129 x 1038030 x 1003458 x 519060 x 501787 x 3460116 x 2595145 x 2076173 x 1740174 x 1730290 x 1038346 x 870348 x 865435 x 692519 x 580
Negative: -1 x -301020-2 x -150510-3 x -100340-4 x -75255-5 x -60204-6 x -50170-10 x -30102-12 x -25085-15 x -20068-20 x -15051-29 x -10380-30 x -10034-58 x -5190-60 x -5017-87 x -3460-116 x -2595-145 x -2076-173 x -1740-174 x -1730-290 x -1038-346 x -870-348 x -865-435 x -692-519 x -580


How do I find the factor combinations of the number 301,020?

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 301,020, 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.

1 301,020
-1 -301,020

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 301,020.

Example:
1 x 301,020 = 301,020
and
-1 x -301,020 = 301,020
Notice both answers equal 301,020

With that explanation out of the way, let's continue. Next, we take the number 301,020 and divide it by 2:

301,020 ÷ 2 = 150,510

If the quotient is a whole number, then 2 and 150,510 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 2 150,510 301,020
-1 -2 -150,510 -301,020

Now, we try dividing 301,020 by 3:

301,020 ÷ 3 = 100,340

If the quotient is a whole number, then 3 and 100,340 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 3 100,340 150,510 301,020
-1 -2 -3 -100,340 -150,510 -301,020

Let's try dividing by 4:

301,020 ÷ 4 = 75,255

If the quotient is a whole number, then 4 and 75,255 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 75,255 100,340 150,510 301,020
-1 -2 -3 -4 -75,255 -100,340 -150,510 301,020
Keep dividing by the next highest number until you cannot divide anymore.

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

1234561012152029305860871161451731742903463484355195806928658701,0381,7301,7402,0762,5953,4605,0175,19010,03410,38015,05120,06825,08530,10250,17060,20475,255100,340150,510301,020
-1-2-3-4-5-6-10-12-15-20-29-30-58-60-87-116-145-173-174-290-346-348-435-519-580-692-865-870-1,038-1,730-1,740-2,076-2,595-3,460-5,017-5,190-10,034-10,380-15,051-20,068-25,085-30,102-50,170-60,204-75,255-100,340-150,510-301,020

More Examples

Here are some more numbers to try:

301,018301,019301,021301,022
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