Q: What are the factor combinations of the number 450,225,307?

 A:
Positive:   1 x 4502253077 x 6431790131 x 14523397217 x 2074771547 x 8230813793 x 1186993829 x 11758316957 x 26551
Negative: -1 x -450225307-7 x -64317901-31 x -14523397-217 x -2074771-547 x -823081-3793 x -118699-3829 x -117583-16957 x -26551


How do I find the factor combinations of the number 450,225,307?

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 450,225,307, 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.

1 450,225,307
-1 -450,225,307

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 450,225,307.

Example:
1 x 450,225,307 = 450,225,307
and
-1 x -450,225,307 = 450,225,307
Notice both answers equal 450,225,307

With that explanation out of the way, let's continue. Next, we take the number 450,225,307 and divide it by 2:

450,225,307 ÷ 2 = 225,112,653.5

If the quotient is a whole number, then 2 and 225,112,653.5 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:

1 450,225,307
-1 -450,225,307

Now, we try dividing 450,225,307 by 3:

450,225,307 ÷ 3 = 150,075,102.3333

If the quotient is a whole number, then 3 and 150,075,102.3333 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:

1 450,225,307
-1 -450,225,307

Let's try dividing by 4:

450,225,307 ÷ 4 = 112,556,326.75

If the quotient is a whole number, then 4 and 112,556,326.75 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:

1 450,225,307
-1 450,225,307
Keep dividing by the next highest number until you cannot divide anymore.

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

17312175473,7933,82916,95726,551117,583118,699823,0812,074,77114,523,39764,317,901450,225,307
-1-7-31-217-547-3,793-3,829-16,957-26,551-117,583-118,699-823,081-2,074,771-14,523,397-64,317,901-450,225,307

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