Q: What are the factor combinations of the number 300,468?

 A:
Positive:   1 x 3004682 x 1502343 x 1001564 x 751176 x 500787 x 4292412 x 2503914 x 2146221 x 1430828 x 1073142 x 715449 x 613273 x 411684 x 357798 x 3066146 x 2058147 x 2044196 x 1533219 x 1372292 x 1029294 x 1022343 x 876438 x 686511 x 588
Negative: -1 x -300468-2 x -150234-3 x -100156-4 x -75117-6 x -50078-7 x -42924-12 x -25039-14 x -21462-21 x -14308-28 x -10731-42 x -7154-49 x -6132-73 x -4116-84 x -3577-98 x -3066-146 x -2058-147 x -2044-196 x -1533-219 x -1372-292 x -1029-294 x -1022-343 x -876-438 x -686-511 x -588


How do I find the factor combinations of the number 300,468?

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 300,468, 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.

1 300,468
-1 -300,468

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 300,468.

Example:
1 x 300,468 = 300,468
and
-1 x -300,468 = 300,468
Notice both answers equal 300,468

With that explanation out of the way, let's continue. Next, we take the number 300,468 and divide it by 2:

300,468 ÷ 2 = 150,234

If the quotient is a whole number, then 2 and 150,234 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 2 150,234 300,468
-1 -2 -150,234 -300,468

Now, we try dividing 300,468 by 3:

300,468 ÷ 3 = 100,156

If the quotient is a whole number, then 3 and 100,156 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 3 100,156 150,234 300,468
-1 -2 -3 -100,156 -150,234 -300,468

Let's try dividing by 4:

300,468 ÷ 4 = 75,117

If the quotient is a whole number, then 4 and 75,117 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 75,117 100,156 150,234 300,468
-1 -2 -3 -4 -75,117 -100,156 -150,234 300,468
Keep dividing by the next highest number until you cannot divide anymore.

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

1234671214212842497384981461471962192922943434385115886868761,0221,0291,3721,5332,0442,0583,0663,5774,1166,1327,15410,73114,30821,46225,03942,92450,07875,117100,156150,234300,468
-1-2-3-4-6-7-12-14-21-28-42-49-73-84-98-146-147-196-219-292-294-343-438-511-588-686-876-1,022-1,029-1,372-1,533-2,044-2,058-3,066-3,577-4,116-6,132-7,154-10,731-14,308-21,462-25,039-42,924-50,078-75,117-100,156-150,234-300,468

More Examples

Here are some more numbers to try:

300,466300,467300,469300,470
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