15 x 14 x 13 x ... x 3 x 2 x 1 = $3^m \times n$. Where m and n are positive integers, then what is the…
15 x 14 x 13 x ... x 3 x 2 x 1 = $3^m \times n$. Where m and n are positive integers, then what is the maximum value of m?
7
6
5
4
Solution
We need the highest power of 3 dividing 15!. Multiples of 3 up to 15 are 3, 6, 9, 12, 15. Counting factors of 3: 3, 6, 12, 15 contribute one 3 each (4 factors) and 9 contributes two 3s, giving $4 + 2 = 6$. Hence the maximum value of m is 6.