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Ans. It could be worthy to move a method to util class if the method needs to be shared, doesn't require polymorphic behavior and need not be overridden in special cases.
Don't belong to one group through is-a relationship ( You can share through parent class method )
Don't implement a specific interface ( java 8 default methods )
Doesn't involve complex computing as you will be loosing the benefit of object state with just static method.
Doesn't require polymorphic behavior as static methods don't participate in runtime polymorphism.
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