What is the greatest integer k such that 80! is divisible by 4^k?
\(\phantom{45^k}\)
80!= 2^78 * 3^36 * 5^19 * 7^12 * 11^7 * 13^6 * 17^4 * 19^4 * 23^3 * 29^2 * 31^2 * 37^2 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 * 73 * 79
k==78 / 2 ==39 ==4^39