🚀 Day 25 of My Automation Journey – Prime Numbers, Reverse Logic & Loops

Today, instead of just writing programs, I focused on understanding the “WHY” behind each logic. Let’s break everything down step by step 👇

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🔹 1. Divisors Logic – Step-by-Step Understanding

💻 Program:

int user = 15;
int i = 0;

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

🧠 Logic Explained:

• i % user == 0 means:
  👉 “Is i divisible by user?”

• Loop runs from 0 → 15

Let’s trace:

i value	i % 15	Condition
0	0	✅ Print
1–14	Not 0	❌ Skip
15	0	✅ Print

📤 Output:

0
15

⚠️ Important Insight:

👉 This program is actually finding multiples of 15 within range, NOT divisors.

✅ Correct Divisor Logic should be:

if (user % i == 0)

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🔹 2. Prime Number Logic – Deep Explanation

💻 Program:

int user = 3;
boolean status = true;
int i = 2;

while(i < user) {
    if(user % i == 0) {
        status = false;
        break;
    }
    i++;
}

if (status==true)
    System.out.println("Prime");
else
    System.out.println("Not a prime");

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🧠 What is a Prime Number?

A number is prime if:

• It has exactly 2 factors → 1 and itself

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🔍 Step-by-Step Flow:

• Start checking from i = 2

• Why?
  👉 Because:

  • Dividing by 1 is always true
  • Dividing by itself is always true So we skip both

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🧪 Example: user = 3

i	Condition (3 % i)	Result
2	3 % 2 ≠ 0	Continue

Loop ends → No divisor found → Prime ✅

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💡 Why boolean status?

• Acts like a flag
• Initially assume → true (prime)
• If any divisor found → false

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⚡ Why break?

• As soon as one divisor is found: 👉 No need to continue checking 👉 Improves performance 🚀

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🔹 3. Reverse Number Logic – Deep Breakdown

💻 Program:

int user = 123;
int reverse = 0;

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

System.out.println(reverse);

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🧠 Core Idea:

We:

1. Extract last digit
2. Append it to reverse
3. Remove last digit

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🔍 Step-by-Step Execution:

Step	user	digit	reverse calculation	reverse
1	123	3	0*10 + 3	3
2	12	2	3*10 + 2	32
3	1	1	32*10 + 1	321

📤 Output:

321

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💡 Key Formula:

reverse = reverse * 10 + digit

👉 This shifts digits left and adds new digit

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🔹 4. While Loop vs For Loop – Conceptual Clarity

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🔁 While Loop

int i = 0;
while(i <= 10) {
    System.out.println(i);
    i++;
}

🧠 Logic:

• Initialization → outside
• Condition → inside while
• Increment → manual

👉 Used when:

• Iterations are unknown
• Condition-based looping

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🔁 For Loop

for(int i = 0; i <= 10; i++) {
    System.out.println(i);
}

🧠 Logic:

• Everything in one line:

  • init, condition, increment

👉 Used when:

• Iterations are known

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📤 Output (Both):

0 1 2 3 4 5 6 7 8 9 10

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🔹 5. Bonus Insight 💡

🖥️ Ctrl + Shift + I

• Auto formats code
• Improves readability
• Saves time in debugging

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🔚 Final Takeaways

✔ % operator is key for divisibility logic
✔ Prime = no divisors between 2 and n-1
✔ Boolean is best for true/false conditions
✔ Reverse logic = extract + rebuild
✔ Loops = backbone of logic building

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🔥 The more you trace step-by-step, the stronger your logic becomes!