Permutations & Combinations
Exponent of prime in factorial
nta_pyq_2025_apr
Grade 12
Question:
The largest n$\i_n N such that 3 divides 50$! is: n
Step-by-Step Solution
Key Concept: Use Legendre’s formula for the exponent of$3$in$50!$.
2$\alpha$$\cdot 3$$\beta$$\cdot 5$$\gamma$(2)$B =$[ 50 ] + [ 50 2 ] + [ 50 3 ] + [ 50 4 ] 3 3 3$3 = 16 + 5 + 1 = 2$Maximum value of n is 22
Correct Answer: 2