At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Dinesh get lockers with the numbers 100, 400, 150, and 420, respectively, who is the most popular student?  Select the correct option:
A) Baskar  B) They have equal popularity  C) Dinesh  D) Raja  E) Kamal
Distinct prime factors of 100 (Raja) : 2,5   Distinct prime factors of 400 (Kamal): 2 and 5.   Distinct prime factors of 150 (Baskar): 2,3, and 5   Distinct prime factors of 420 (Dinesh): 2,3,5 and 7.   So most popular student - Dinesh   Answer Dinesh
<result>C</result>
At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Raja,Kamal, Baskar, and Dinesh get lockers with the numbers 100, 400, 150, and 420, respectively, who is the most popular student?