# 🚀 Day 25 of My Automation Journey – Deep Dive into Logic (Part 2)

Continuing from earlier, here are the remaining core number programs with full step-by-step explanations to strengthen logic building 👇

---

🔹 6. Divisors of a Number – Correct Logic

💻 Program:

int user = 15;

for(int i = 1; i <= user; i++) {
    if(user % i == 0)
        System.out.println(i);
}

---

🧠 Logic Explained:

• user % i == 0 means:
  👉 “Can i divide user without remainder?”

• Loop runs from 1 → 15

---

🔍 Step-by-Step Trace:

i	15 % i	Result
1	0	✅ Print
2	1	❌
3	0	✅
4	3	❌
5	0	✅
15	0	✅

---

📤 Output:

1 3 5 15

---

💡 Key Insight:

👉 Divisors are numbers that perfectly divide the given number

---

🔹 7. Count of Divisors

💻 Program:

int user = 15;
int count = 0;

for(int i = 1; i <= user; i++) {
    if(user % i == 0)
        count++;
}

System.out.println(count);

---

🧠 Logic Explained:

• Same logic as divisors
• Instead of printing → we count

---

🔍 Example:

Divisors of 15 → 1, 3, 5, 15

👉 Count = 4

---

📤 Output:

4

---

💡 Key Insight:

👉 Reuse logic + add counter → powerful pattern

---

🔹 8. Count of Digits

💻 Program:

int user = 12345;
int count = 0;

while(user > 0) {
    user = user / 10;
    count++;
}

System.out.println(count);

---

🧠 Logic Explained:

• Each division by 10 removes one digit

---

🔍 Step-by-Step:

Step	user	count
1	12345 → 1234	1
2	1234 → 123	2
3	123 → 12	3
4	12 → 1	4
5	1 → 0	5

---

📤 Output:

5

---

💡 Key Insight:

👉 Number of times you divide = number of digits

---

🔹 9. Sum of Digits

💻 Program:

int user = 123;
int sum = 0;

while(user > 0) {
    int digit = user % 10;
    sum = sum + digit;
    user = user / 10;
}

System.out.println(sum);

---

🧠 Logic Explained:

We do 3 operations:

1. Extract last digit → % 10
2. Add to sum
3. Remove digit → / 10

---

🔍 Step-by-Step:

Step	digit	sum	user
1	3	3	12
2	2	5	1
3	1	6	0

---

📤 Output:

6

---

💡 Key Insight:

👉 % 10 and / 10 are the backbone of number problems

---

🔹 10. Palindrome Number

💻 Program:

int user = 121;
int original = user;
int reverse = 0;

while(user > 0) {
    int digit = user % 10;
    reverse = reverse * 10 + digit;
    user = user / 10;
}

if(original == reverse)
    System.out.println("Palindrome");
else
    System.out.println("Not Palindrome");

---

🧠 Logic Explained:

👉 A palindrome reads the same forward and backward

---

🔍 Step-by-Step:

Step	digit	reverse	user
1	1	1	12
2	2	12	1
3	1	121	0

---

📤 Output:

Palindrome

---

❌ Non-Palindrome Example:

123 → reverse = 321 → Not equal

---

💡 Key Formula:

reverse = reverse * 10 + digit

---

🔚 Final Takeaways

✔ Divisors → user % i == 0
✔ Count → reuse + increment
✔ Digits → / 10 removes digits
✔ Sum → % 10 extracts digits
✔ Palindrome → reverse + compare

---

💡 Golden Rule

👉 Almost ALL number-based problems depend on:

% 10  → Extract last digit
/ 10  → Remove last digit

Master this → you unlock most logic problems 🚀

---

🔥 Consistency + tracing logic = strong programming foundation!