Q.1) Express each number as a product of its prime factors:
(i). 140

(ii). 156

(iii). 3825

(iv). 5005

(v). 7429

How to stay motivated to study every day
The world outside your window is a carnival of distractions, a siren’s call of instant gratification. Your phone buzzes with the promise of social connection, your streaming service offers an escape into another world, and your bed seems to possess a gravitational pull of its own. In this cacophony of modern life, the quiet, solitary act of studying can feel like the most unnatural thing you could possibly do.
Yet, it is within this very act—this deliberate, focused engagement with knowledge—that the entire architecture of your future is built. Motivation, in its purest form, is not some magical lightning bolt that strikes the chosen few. It is a fire. And like any fire, you must learn to build it, stoke it, and protect it from the wind. You must create the conditions for it to burn every single day.
So, let’s get to work. This is your masterclass in building an unshakable daily study habit.
Part I: The Fuel – Forging Your Ultimate “Why”
Before you even open a book, you must answer the most critical question of all: Why? Not the surface-level “because I need a degree” or “because I want a good job.” Those are destinations, not motivations. They are the destination you see on a map, but they don’t tell you why you want to go there.
Your ultimate “why” must be forged in the fire of your deepest emotions. Why do you really want this?
- Is it to prove to yourself that you are capable of mastery?
- Is it to build a life of security and freedom for your family?
- Is it to solve a problem in the world that you are deeply passionate about?
- Is it to build a new identity, to become the person you’ve always admired?
Grab a piece of paper, or open a new document. Write down your “why.” Now, write it again, but this time, make it visceral. Use words that evoke emotion. Instead of “I want to be a doctor,” write, “I want to be the person a terrified patient looks to in their darkest moment, knowing they can be saved.” This isn’t just a goal; it’s a compass.
Visualize the Victory: Spend just five minutes a day visualizing your success. Close your eyes and see yourself receiving your diploma, getting that promotion, or solving that complex problem. Feel the pride swelling in your chest. Taste the satisfaction. This isn’t idle daydreaming; it’s mental rehearsal. Your brain doesn’t know the difference between a vividly imagined experience and a real one. By regularly visualizing success, you are programming your brain for it. You are building the neurological pathways that will drive you forward when the road gets tough.
Part II: The Strategy – How to Build a System, Not Just a Goal
Goals are about the result you want to achieve. Systems are about the process that gets you there. A goal is to write a book; a system is a daily writing habit of 500 words. When you are motivated, you can focus on the goal. But on a rainy Tuesday afternoon when your motivation is flagging, you don’t need a goal; you need a system you can trust.
1. The Art of the Atomic Habit:
Stop telling yourself you need to “study for hours.” It’s too big, too abstract, and frankly, too daunting. Instead, shrink the action down to its smallest possible unit. Make it so small and easy that you can’t say no.
- Instead of “study biology,” make it “read and highlight one page.”
- Instead of “write my essay,” make it “write the first sentence.”
- Instead of “review notes,” make it “recall one key concept out loud.”
This is the power of “atomic habits.” Your goal is not to read 50 pages; your goal is to sit down and read one page. Once you do that, the momentum often carries you forward. You’re no longer battling the psychological weight of a monumental task; you’re just doing one simple, manageable thing. Consistency is infinitely more powerful than intensity. A small, daily action repeated over time creates a force stronger than a once-a-week marathon study session.
2. Design Your Environment:
You are a product of your environment. If your study space is a mess, you will feel chaotic. If your phone is on your desk, you will be distracted. You cannot rely on willpower to overcome a poorly designed environment.
- Clean up: Start with a clean desk. It sends a signal to your brain that it is time for focus.
- The “Phone Jail”: Your phone is a nuclear weapon of mass distraction. When you study, put it in another room, or in a drawer on silent. If you need it for music, put it on “Do Not Disturb” and place it out of arm’s reach.
- Curate Your Space: Have everything you need—pens, highlighters, water, sticky notes—within arm’s reach. Create a sensory experience that invites focus. Light a candle, put on some instrumental music, or simply open the window for fresh air. Make your study space a sanctuary of productivity.
3. The Power of Rhythm:
Your brain isn’t a machine that can run on full power for eight hours straight. It operates in cycles. This is where the Pomodoro Technique shines. Here’s a slightly adapted version:
- Focus (25 minutes): Give your absolute, undivided attention to your task.
- Break (5 minutes): Step away. Do not scroll on social media. Instead, stretch, walk around, grab a glass of water, do a few push-ups. Let your brain subconsciously process what you just learned.
- Long Break (15-20 minutes): After four “Pomodoros,” take a longer break to recharge.
This isn’t about just managing time; it’s about managing your energy. By respecting your brain’s rhythms, you work smarter, not harder.
Part III: The Mindset – Fortifying the Mental Fortress
The path of a student is littered with the debris of discouragement. You will fail a practice test. You will struggle to understand a concept. You will have days where it feels like the knowledge is going in one ear and out the other. This is not a sign of weakness; it is a sign of learning. The key is how you respond.
1. Cultivate a Growth Mindset:
Dr. Carol Dweck’s research on mindset is a game-changer. A fixed mindset believes your intelligence is static—you’re either born smart or you aren’t. A growth mindset believes that your intelligence and abilities can be developed through hard work and dedication.
- When you struggle: Instead of thinking, “I’m just not good at this,” rephrase it to, “I haven’t mastered this yet.”
- When you fail: Instead of seeing it as a verdict on your potential, see it as data. “What did I get wrong and how can I learn from it?” Failure is not the opposite of success; it is a part of the process of success.
2. Love the Process, Not Just the Prize:
The joy of learning is often underestimated. Stop seeing your textbooks as a chore to be endured and start seeing them as a key that unlocks a new level in the game of life. When you’re reading, try to find something genuinely interesting. Look for a connection to the real world. Ask questions. Make learning an act of curiosity, not just a task to be completed.
3. The Power of the “Ritual”:
Human beings are creatures of habit. Create a pre-study ritual to tell your brain that it’s time to shift gears. This could be:
- Making a cup of tea or coffee.
- Lighting a candle.
- Doing a two-minute breathing exercise.
- Putting on a specific pair of headphones and a “focus” playlist.
This ritual becomes a mental trigger. Every time you perform it, you’re priming your mind to enter a state of deep focus.
Part IV: The Encore – Self-Care as a Strategy
You are not a machine. Your brain is a biological organ that needs fuel, rest, and maintenance. Studying on an empty tank is a recipe for burnout.
- Sleep: This is non-negotiable. Your brain consolidates memories during sleep. Without it, you might as well be studying with a hole in your head. Aim for 7-8 hours of quality sleep.
- Movement: Exercise isn’t just for your body; it’s for your brain. It releases endorphins, improves focus, and reduces stress. A 20-minute walk in the middle of your study day can be a game-changer.
- Fuel: What you eat affects your ability to focus. Protein, healthy fats, and complex carbohydrates are your brain’s best friends. Avoid the sugar crash.
- Reward Yourself: Celebrate the small wins! Finished a difficult chapter? Rewarded yourself with an episode of your favorite show. Stuck to your study schedule for a week? Treat yourself to a nice dinner. These rewards create a positive feedback loop and make the process something to look forward to.
Part V: The Final Word – You Are the Architect
Ultimately, motivation is a decision you make. It is a promise you keep to the person you are striving to become. It is a discipline you practice until it becomes a habit.
On the days you don’t feel like it—and there will be many—remember your “why.” Trust the system you’ve built. The journey of a thousand miles begins with a single step, and that step is today, right now.
You have the power to shape your future. The knowledge you are acquiring is not just a collection of facts; it is the foundation of a new world. It is the key to becoming the person you were meant to be.
So, get started. Turn off the noise. Open your book. Take that first, small step. Your future self is watching, and they are cheering you on. They are counting on you to make this the day that everything changes. Make it count.
Now, go. The world is waiting for the person you are about to become.
