Problem
NT-B2-M05-P015 Exponent in a Quotient
#15
★★★★☆ Level 4 of 5
Find \(v_2\left(\frac{100!}{50!}\right)\).
Subtract \(v_2(50!)\) from \(v_2(100!)\).
\(v_2(100!)=97\), \(v_2(50!)=25+12+6+3+1=47\). Therefore the required exponent is \(97-47=50\).
Useful for products from \(51\) to \(100\).