If 15 to the power and where n is a natural number is divisible by 25 what is the least value of n
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Given : 15ⁿ is divisible by 25
To find : the least value of n
Solution:
15ⁿ is divisible by 25
= > 15ⁿ/25 is an integer
= (3 * 5)ⁿ/5* 5
= 3ⁿ * 5ⁿ / 5²
3 & 5 are co prime
=> 5ⁿ = k . 5² ( k being an integer )
For least value of n k must be 1
=> 5ⁿ = 1 . 5²
=> 5ⁿ = 5²
=> n = 2
Least value on n Should be 2
15² /25
= 225/25
= 9
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