Question

What is highest power of 6 contained in 25!​

Answer 1

Answer:

25⁶

Step-by-step explanation:

Answer 2

Answer:

Highest power of 6 contained in 25!​ =10

Step-by-step explanation:

Step 1: Express 6 in terms of its prime factors

            6=3×2

Step 2: Among the two prime factors, the maximum of larger prime number will always be less than the maximum of of lower prime factor. Accordingly, among the prime factors 3 and 2, highest power of 3 in 25! Will be less than the highest power of 2 in 25!.

Hence the highest power of 6 in 25! will be equal to the highest power of 3 in 25 !

$25!=6^{k} \\k=?$

$25 !=\left[\frac{25}{3^{1} }\right]+\left[\frac{25}{3^{2}}\right]+\left[\frac{25}{3^{3}}\right]\\=8+2+0\\=10$

Highest power of 3 is 10.

Hence the highest power of 6 in 25!=10