A natural number n such that n ! ends in exactly 1000 zeros is

Step-by-step solution

Option 1 n = 4010 4010 5 + 4010 25 + 4010 125 + 4010 625 + 4010 3125 = 802 + 160 + 32 + 6 + 1 = 1001 > 1000 Option 2 4000 5 + 4000 25 + 4000 125 + 4000 625 + 4000 3125 = 800 + 160 + 32 + 6 + 1 = 999 < 1000 Option 3 4009 5 + 4009 25 + 4009 125 + 4009 625 + 4009 3125 = 801 + 160 + 32 + 6 + 1 = 1000 Option 4 4004 5 + 4004 25 + 4004 125 + 4004 625 + 4004 3125 = 800 + 160 + 32 + 6 + 1 = 999 < 1000