Q: What are the factor combinations of the number 301,450,435?

 A:
Positive:   1 x 3014504355 x 6029008711 x 2740458513 x 2318849555 x 548091765 x 4637699143 x 2108045715 x 421609
Negative: -1 x -301450435-5 x -60290087-11 x -27404585-13 x -23188495-55 x -5480917-65 x -4637699-143 x -2108045-715 x -421609


How do I find the factor combinations of the number 301,450,435?

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 301,450,435, 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.

1 301,450,435
-1 -301,450,435

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 301,450,435.

Example:
1 x 301,450,435 = 301,450,435
and
-1 x -301,450,435 = 301,450,435
Notice both answers equal 301,450,435

With that explanation out of the way, let's continue. Next, we take the number 301,450,435 and divide it by 2:

301,450,435 ÷ 2 = 150,725,217.5

If the quotient is a whole number, then 2 and 150,725,217.5 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:

1 301,450,435
-1 -301,450,435

Now, we try dividing 301,450,435 by 3:

301,450,435 ÷ 3 = 100,483,478.3333

If the quotient is a whole number, then 3 and 100,483,478.3333 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:

1 301,450,435
-1 -301,450,435

Let's try dividing by 4:

301,450,435 ÷ 4 = 75,362,608.75

If the quotient is a whole number, then 4 and 75,362,608.75 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:

1 301,450,435
-1 301,450,435
Keep dividing by the next highest number until you cannot divide anymore.

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

1511135565143715421,6092,108,0454,637,6995,480,91723,188,49527,404,58560,290,087301,450,435
-1-5-11-13-55-65-143-715-421,609-2,108,045-4,637,699-5,480,917-23,188,495-27,404,585-60,290,087-301,450,435

More Examples

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