Q: What are the factor combinations of the number 301,628,344?

 A:
Positive:   1 x 3016283442 x 1508141724 x 754070868 x 3770354319 x 1587517638 x 793758876 x 3968794152 x 1984397
Negative: -1 x -301628344-2 x -150814172-4 x -75407086-8 x -37703543-19 x -15875176-38 x -7937588-76 x -3968794-152 x -1984397


How do I find the factor combinations of the number 301,628,344?

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 301,628,344, 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.

1 301,628,344
-1 -301,628,344

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 301,628,344.

Example:
1 x 301,628,344 = 301,628,344
and
-1 x -301,628,344 = 301,628,344
Notice both answers equal 301,628,344

With that explanation out of the way, let's continue. Next, we take the number 301,628,344 and divide it by 2:

301,628,344 ÷ 2 = 150,814,172

If the quotient is a whole number, then 2 and 150,814,172 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 2 150,814,172 301,628,344
-1 -2 -150,814,172 -301,628,344

Now, we try dividing 301,628,344 by 3:

301,628,344 ÷ 3 = 100,542,781.3333

If the quotient is a whole number, then 3 and 100,542,781.3333 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 2 150,814,172 301,628,344
-1 -2 -150,814,172 -301,628,344

Let's try dividing by 4:

301,628,344 ÷ 4 = 75,407,086

If the quotient is a whole number, then 4 and 75,407,086 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 4 75,407,086 150,814,172 301,628,344
-1 -2 -4 -75,407,086 -150,814,172 301,628,344
Keep dividing by the next highest number until you cannot divide anymore.

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

12481938761521,984,3973,968,7947,937,58815,875,17637,703,54375,407,086150,814,172301,628,344
-1-2-4-8-19-38-76-152-1,984,397-3,968,794-7,937,588-15,875,176-37,703,543-75,407,086-150,814,172-301,628,344

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