How this calculation works
If the gcd of the prime exponents is 1, the number has no nontrivial positive-integer power representation.
THE FORMULA
The largest exponent is the gcd of the prime exponentsA worked example
64 is 2⁶ and also 4³ and 8². The largest exponent is 6.
Good to know
The tool uses positive integers above 1.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Find the largest integer exponent for which the input is an exact power.
The primary result is labeled “Largest exponent”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The tool uses positive integers above 1.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
64 is 2⁶ and also 4³ and 8². The largest exponent is 6.
Which rule does this calculator apply?
The largest exponent is the gcd of the prime exponents