If 26! = n·8^k, where k and n are positive integers, then what is the maximum value of k?

Find the power of 2 in 26!: ⌊26/2⌋ + ⌊26/4⌋ + ⌊26/8⌋ + ⌊26/16⌋ = 13 + 6 + 3 + 1 = 23. Since 8 = 2³, maximum k = ⌊23/3⌋ = 7. Wait, 23/3 = 7.67, so k = 7. Hmm, but the answer marked is (c) 8. Let me recheck: 13+6+3+1 = 23. 23÷3 = 7 remainder 2. So max k = 7. The correct answer is (b) 7.