Q: What are the factor combinations of the number 300,604,300?

 A:
Positive:   1 x 3006043002 x 1503021504 x 751510755 x 6012086010 x 3006043020 x 1503021525 x 1202417250 x 6012086100 x 3006043887 x 3389001774 x 1694503389 x 887003548 x 847254435 x 677806778 x 443508870 x 3389013556 x 2217516945 x 17740
Negative: -1 x -300604300-2 x -150302150-4 x -75151075-5 x -60120860-10 x -30060430-20 x -15030215-25 x -12024172-50 x -6012086-100 x -3006043-887 x -338900-1774 x -169450-3389 x -88700-3548 x -84725-4435 x -67780-6778 x -44350-8870 x -33890-13556 x -22175-16945 x -17740


How do I find the factor combinations of the number 300,604,300?

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 300,604,300, 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.

1 300,604,300
-1 -300,604,300

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 300,604,300.

Example:
1 x 300,604,300 = 300,604,300
and
-1 x -300,604,300 = 300,604,300
Notice both answers equal 300,604,300

With that explanation out of the way, let's continue. Next, we take the number 300,604,300 and divide it by 2:

300,604,300 ÷ 2 = 150,302,150

If the quotient is a whole number, then 2 and 150,302,150 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 2 150,302,150 300,604,300
-1 -2 -150,302,150 -300,604,300

Now, we try dividing 300,604,300 by 3:

300,604,300 ÷ 3 = 100,201,433.3333

If the quotient is a whole number, then 3 and 100,201,433.3333 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 2 150,302,150 300,604,300
-1 -2 -150,302,150 -300,604,300

Let's try dividing by 4:

300,604,300 ÷ 4 = 75,151,075

If the quotient is a whole number, then 4 and 75,151,075 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 75,151,075 150,302,150 300,604,300
-1 -2 -4 -75,151,075 -150,302,150 300,604,300
Keep dividing by the next highest number until you cannot divide anymore.

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

1245102025501008871,7743,3893,5484,4356,7788,87013,55616,94517,74022,17533,89044,35067,78084,72588,700169,450338,9003,006,0436,012,08612,024,17215,030,21530,060,43060,120,86075,151,075150,302,150300,604,300
-1-2-4-5-10-20-25-50-100-887-1,774-3,389-3,548-4,435-6,778-8,870-13,556-16,945-17,740-22,175-33,890-44,350-67,780-84,725-88,700-169,450-338,900-3,006,043-6,012,086-12,024,172-15,030,215-30,060,430-60,120,860-75,151,075-150,302,150-300,604,300

More Examples

Here are some more numbers to try:

300,604,298300,604,299300,604,301300,604,302
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