Which of these numbers has the most number of divisors?

Correct option is B

Option(a) 200:

$$200 = 2^3 \times5^2$$

Number of divisors = (3+1)(2+1) = 12 

Option(b) 240

​$$240 = 2^4\times3^1\times5^1$$

Numbers of divisors = (4+1)(1+1)(1+1)

                              = 20 

Option(c) 156

​$$156 = 2^2\times3^1\times13^1$$​​

Numbers of divisors = (2+1)(1+1)(1+1) 

                                = 12 

Option(d)172

​$$172 = 2^2\times43^1$$

Number of divisors = (2+1)(1+1)

                              = 6 

Hence, 240 has the most number of divisors. 

option (b) is correct.