what is the greatest positive power of 5 that exactly divides 30!
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Another way of asking the question is, what is the highest power of 5 in 30!.
The highest power of prime number p in n! = (n/p¹) + (n/p²) + (n/p³) + (n/p⁴) +....
So, the greatest power of 5 which can divide 30! exactly
= (30/5¹) + (30/5²)
= 6 + 1
= 7
Answer
Another way of asking the question is, what is the highest power of 5 in 30!.
The highest power of prime number p in n! = (n/p¹) + (n/p²) + (n/p³) + (n/p⁴) +....
So, the greatest power of 5 which can divide 30! exactly
= (30/5¹) + (30/5²)
= 6 + 1
= 7
Answer
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