The number of common prime factors of 75, 60 and 105 is
2
3
4
5
Step 1: Understand the task
We need the prime factors that are common to all three numbers.
Step 2: Prime factorize 75
75 = 3 × 25
25 = 5 × 5
So, 75 = 3 × 5 × 5 = (3 imes 5^2).
Step 3: Prime factorize 60
60 = 6 × 10
6 = 2 × 3
10 = 2 × 5
So, 60 = 2 × 2 × 3 × 5 = (2^2 imes 3 imes 5).
Step 4: Prime factorize 105
105 = 3 × 35
35 = 5 × 7
So, 105 = 3 × 5 × 7 = (3 imes 5 imes 7).
Step 5: List prime factors
75 → {3, 5}
60 → {2, 3, 5}
105 → {3, 5, 7}
Step 6: Find common primes
Common to all three: {3, 5}.
Step 7: Count them
There are 2 common prime factors.
Answer: 2 (Option A)