How do I find the factor combinations of the number 657,240,600?
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 657,240,600, 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 |
|
657,240,600 |
-1 |
|
-657,240,600 |
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 657,240,600.
Example:
1 x 657,240,600 = 657,240,600
and
-1 x -657,240,600 = 657,240,600
Notice both answers equal 657,240,600
With that explanation out of the way, let's continue. Next, we take the number 657,240,600 and divide it by 2:
657,240,600 ÷ 2 = 328,620,300
If the quotient is a whole number, then 2 and 328,620,300 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:
Now, we try dividing 657,240,600 by 3:
657,240,600 ÷ 3 = 219,080,200
If the quotient is a whole number, then 3 and 219,080,200 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:
Let's try dividing by 4:
657,240,600 ÷ 4 = 164,310,150
If the quotient is a whole number, then 4 and 164,310,150 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:
Keep dividing by the next highest number until you cannot divide anymore.
If you did it right, you will end up with this table:
More Examples
Here are some more numbers to try:
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