The positive integer 200 has how many factors?

The positive integer 200 has how many factors?

A. 2
B. 10
C. 12
D. 15
E. 24

The OA is C .

Can someone help me with a formula for such type of questions? I would be thankful.

Hi VJesus12,
Let's take a look at your question.

We are asked to find the number of factors of 200.
Let's find the number of factors of 200 step by step.

Step 1:
To find the number of factors of a number we first write the number as a product of its prime factors.
$$200=\ 2\times100$$
$$200=\ 2\times10\times10$$
$$200=\ 2\times2\times5\times2\times5$$


Step 2:
Now write the repeating factors using exponents.
$$200=\ 2^3\times5^2$$


Step 3:
Add one to each exponent and find the product. This product will be equal to the number of factors.
Therefore the number of factors of 200 will be:
$$=\left(3+1\right)\times\left(2+1\right)$$
$$=4\times3=12$$

Therefore, there are 12 factors of 200.
Hence, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.