Problem
NT-B2-M05-P010 Base \(12\)
#10
★★★☆☆ Level 3 of 5
How many trailing zeros does \(100!\) have in base \(12\)?
Find the largest \(k\) such that \(12^k\mid100!\).
Since \(12=2^2\cdot3\), the number of zeros is \(\min(\lfloor v_2(100!)/2\rfloor, v_3(100!))=\min(48,48)=48\).
Important for the later module on bases.