How many factors of $$2^2×3^1×5^2×7^1$$ are divisible by 50 but not by 100?​

Correct option is A

​Given:

​$$N = 2^2 \times 3^1 \times 5^2 \times 7^1$$​​

Formula Used:
A factor divisible by 50 must include $$2^1 \times 5^2$$​​
To not be divisible by 100, it must not include 2² ​

For counting number of total factors for any number:

​$$A^x \times B^y = (x+1)\times(y+1)$$ = total factors  ​

Solution:
Fixing 2¹ and 5²,  to make the number divisible by 50 and not divisible by 100

Now,  counting  possibilities for 3¹ and 7¹

3¹: 1 + 1 ( power + 1) = 2 

7¹: 1 + 1 ( power + 1) = 2 

2²: not included as it make the number divisible by 100 

Thus

Total factors: 2 × 2 = 4