Calculation:If 15a divides 46! without leaving any remainder,? 15a will be a factor of 46!46! = 1 × 2 × 3 × 4 × .............× 46Factorisation will give the following. 46! = k × 3b × 5c Since we need to find the power of 15 only need to consider factors of 15.b = [46/3] + [46/9] + [46/27] + [46/81] + .......... ([a] is the greatest integer function)? b = 15 + 5 + 1 = 21Similalry,c = [46/5] + [46/25] + [46/125] + .........? c = 9 + 1 = 10? 46! = k × 321 × 510? 46! = k × 311 × (3 × 5)10? Max(a) = 10If n! = pa × qb, then a = [n/p] + [n/p2] + [n/p3] + ............, where [x] is the greatest integer function.In these types of questions try to factorise the number in place of the divisor (in this case 15), and find the powers of those factors. Go for the factor which can possibly have the lowest power (in this case 5).