Q: What are the factor combinations of the number 200,310,625?

 A:
Positive:   1 x 2003106255 x 4006212525 x 801242541 x 4885625125 x 1602485205 x 977125625 x 3204971025 x 1954255125 x 390857817 x 25625
Negative: -1 x -200310625-5 x -40062125-25 x -8012425-41 x -4885625-125 x -1602485-205 x -977125-625 x -320497-1025 x -195425-5125 x -39085-7817 x -25625


How do I find the factor combinations of the number 200,310,625?

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 200,310,625, 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.

1 200,310,625
-1 -200,310,625

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 200,310,625.

Example:
1 x 200,310,625 = 200,310,625
and
-1 x -200,310,625 = 200,310,625
Notice both answers equal 200,310,625

With that explanation out of the way, let's continue. Next, we take the number 200,310,625 and divide it by 2:

200,310,625 ÷ 2 = 100,155,312.5

If the quotient is a whole number, then 2 and 100,155,312.5 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:

1 200,310,625
-1 -200,310,625

Now, we try dividing 200,310,625 by 3:

200,310,625 ÷ 3 = 66,770,208.3333

If the quotient is a whole number, then 3 and 66,770,208.3333 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:

1 200,310,625
-1 -200,310,625

Let's try dividing by 4:

200,310,625 ÷ 4 = 50,077,656.25

If the quotient is a whole number, then 4 and 50,077,656.25 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:

1 200,310,625
-1 200,310,625
Keep dividing by the next highest number until you cannot divide anymore.

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

1525411252056251,0255,1257,81725,62539,085195,425320,497977,1251,602,4854,885,6258,012,42540,062,125200,310,625
-1-5-25-41-125-205-625-1,025-5,125-7,817-25,625-39,085-195,425-320,497-977,125-1,602,485-4,885,625-8,012,425-40,062,125-200,310,625

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