it is due to difference in number of electrons participating in reactions

KMnO4 + 8H+ + 5 electrons .........>K+ +Mn2+ +4H2O (ACIDIC MEDIUM)

KMnO4 +2H2O+3eletrons..........>K+ +4OH- +MnO2 (ALKALINE MEDIUM)

KMnO4 has a Molar mass of 158.04 g/mol

to find its equivalent weight as an oxidizer we need to divide the Molar mass by the moles of electrons taken in its half reaction
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the less common half reaction, uses KMnO4 as an oxidizer in an basic solution:
KMnO4 (takes 3 electrons) & OH- --> MnO2 (s)

in which case your answer comes form:
158.04 g/mol divided by 3 moles of e- =
Your less commonly used answer = 52.68 grams / equivalent
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the most common half reaction, uses KMnO4 as an oxidizer in an acidic solution:
KMnO4 (takes 5 electrons) & 8 H+ --> Mn+2

in which case your answer comes form:
158.04 g/mol divided by 5 moles of e- =
Your most widely used answer = 31.61 grams / equivalent

hello dear