Extracting Integer value from Object Java

There are two ways to deal with the problem. Also, you can simplify your code by using Math.max.

1. Replace the raw type with the parameterized type (the recommended way):

import java.util.HashMap;
import java.util.Map;
import java.util.Map.Entry;

public class Main {
    public static void main(String[] args) {
        System.out.println(maxFrequencyNumber(new int[] { 10, 20, 30, 10, 30, 40, 10, 20, 30, 40, 10 }));
    }

    public static int maxFrequencyNumber(int[] arr) {
        Map<Integer, Integer> m = new HashMap<>();
        for (int i : arr) {
            m.put(i, m.getOrDefault(i, 0) + 1);
        }
        int num, max = Integer.MIN_VALUE;
        for (Entry<Integer, Integer> e : m.entrySet()) {
            max = Math.max(max, e.getValue());
        }
        return max;
    }
}

2. Cast e.getValue() to (Integer):

import java.util.HashMap;
import java.util.Map;

public class Main {
    public static void main(String[] args) {
        System.out.println(maxFrequencyNumber(new int[] { 10, 20, 30, 10, 30, 40, 10, 20, 30, 40, 10 }));
    }

    public static int maxFrequencyNumber(int[] arr) {
        Map<Integer, Integer> m = new HashMap<>();
        for (int i : arr) {
            m.put(i, m.getOrDefault(i, 0) + 1);
        }
        int num, max = Integer.MIN_VALUE;
        for (Map.Entry e : m.entrySet()) {
            max = Math.max(max, (Integer) e.getValue());
        }
        return max;
    }
}

Output:

4

Additional note: Since you do not need keys in the map, you could simply iterate Map::values as follows:

import java.util.HashMap;
import java.util.Map;

public class Main {
    public static void main(String[] args) {
        System.out.println(maxFrequencyNumber(new int[] { 10, 20, 30, 10, 30, 40, 10, 20, 30, 40, 10 }));
    }

    public static int maxFrequencyNumber(int[] arr) {
        Map<Integer, Integer> m = new HashMap<>();
        for (int i : arr) {
            m.put(i, m.getOrDefault(i, 0) + 1);
        }
        int num, max = Integer.MIN_VALUE;
        for (Integer i : m.values()) {
            max = Math.max(max, i);
        }
        return max;
    }
}

You defined a Map<Integer, Integer> map so you can iterate over its keys erasing your Map.Entry problem like below:

int num, max = Integer.MIN_VALUE;
for (Integer key : m.keySet()) {
    int value = m.get(key);
    if (value > max) {
        num = key;
        max = value;
    }
}

Your codes with casting

  public static int maxFrequencyNumber(int[] arr){
      Map<Integer,Integer> m = new HashMap<>();
      for(int i:arr)
          m.put(i,m.getOrDefault(i,0)+1);
      int num,max=Integer.MIN_VALUE;
      for(Map.Entry e:m.entrySet()){
          if(((Integer)e.getValue()).intValue()>max){
              num=((Integer)e.getKey()).intValue();
              max=((Integer)e.getValue()).intValue();
          }
      }
      return max; 
  }