isi-entrance 2014 Q12

isi-entrance · India · solved Number Theory Divisibility and Divisor Analysis
Let $P = \{2^a \cdot 3^b : 0 \leq a, b \leq 5\}$. Find the largest $n$ such that $2^n$ divides some element of $P$.
(A) $n = 20$ (B) $n = 22$ (C) $n = 24$ (D) $n = 26$
(C) $n = 24$
Let $P = \{2^a \cdot 3^b : 0 \leq a, b \leq 5\}$. Find the largest $n$ such that $2^n$ divides some element of $P$.

(A) $n = 20$ \quad (B) $n = 22$ \quad (C) $n = 24$ \quad (D) $n = 26$