Problem
NT-B2-M05-P005 Twos in \(100!\)
#5
★★☆☆☆ Level 2 of 5
Find the largest \(k\) such that \(2^k\mid100!\).
This is \(v_2(100!)\).
\(v_2(100!)=50+25+12+6+3+1=97\). Thus the largest \(k\) is \(97\).
Good check of Legendre's formula.