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      • Maxima and Minima
      • Rolle's Theorem
      • Tangents and Normals
      • Integration by Partial Fractions
      • Integration of Particular Functions
      • Integration Using Trigonometric Identities
      • Integral of e^x[f(x) + f'(x)]
      • Finding the Area Bounded by a Curve
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      • Finding the Position Vector of a Point
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      • Angle Between a Line and a Plane
      • Shortest Distance Between Two Lines
      • Area of a Triangle and Parallelogram Using Vectors
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      • Data Interpretation: Bar Graphs
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      • Operations on Matrices
      • Special Types of Matrices
      • Symmetric and Skew-Symmetric Matrices
      • Square Matrix Properties
      • Solving a System of Equations with Matrices
      • Area of a Triangle Using Determinants
    • Math: Sets, Relations and Functions
      • Types of Relations
      • Types of Functions
      • Binary Operation
      • Composition of Functions (gof and fog)
      • Operations on Sets
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      • Area and Perimeter Formulas Reference
      • Surface Area and Volume Formulas Reference
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      • Trigonometry Basics
      • Inverse Trigonometric Functions
      • Degrees and Radians
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      • Wave Optics: Young's Double Slit Experiment
      • Diffraction: Single Slit and Diffraction Grating
      • Photoelectric Effect
      • de Broglie Wavelength and Matter Waves
    • Engineering Mathematics
      • Laplace Transforms
      • Fourier Series
      • Eigenvalues and Eigenvectors
      • Partial Differentiation
      • Vector Calculus: Gradient, Divergence, and Curl
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      • Logic Gates
      • Boolean Algebra
      • Stack (Data Structure)
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      • Kirchhoff's Current and Voltage Laws
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      • Thevenin's and Norton's Theorems
      • Transistor Biasing
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        • 6 JEE/NEET Myths That Are Actually Wrong (or Just Outdated)
        • Should You Drop a Year for JEE/NEET? A Framework, Not a Feeling
        • 4 Silly Mistakes Costing You Marks in JEE/NEET (and How to Fix Each One)
        • How to Revise Your Entire JEE/NEET Syllabus in the Last 30 Days
        • 5 Rules for a JEE/NEET Study Timetable That Doesn't Burn You Out
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        • How Far Does the Fermi Level Move When You Dope Silicon?
        • How Many Flip-Flops Does a Mod-N Counter Need?
        • Why Does a Zener Diode Hold Its Voltage, and When Does It Stop?
        • Why Can't AM Put More Than a Third of Its Power in the Sidebands?
        • How Does a Diode's Small-Signal Resistance Change With Bias Current?
        • Why Does the Early Effect Give a BJT a Finite Output Resistance?
        • Why Does a Fourier Series Overshoot by 9% at Every Jump?
        • How Does a Hamming (7,4) Syndrome Point to the Flipped Bit?
        • What Do Students Get Wrong About Don't-Cares in K-Maps?
        • How Much Does the Miller Effect Cut Common-Emitter Bandwidth?
        • How Does the Nyquist Criterion Handle a Pole on the jω Axis?
        • Why Does an Op-Amp Integrator Saturate, and How Long Does It Take?
        • What Do You Do When a Routh Array Has a Zero in the First Column?
        • Why Does Resistance Lower Q in Series RLC but Raise It in Parallel?
        • How Do You Calculate Setup and Hold Slack for a Flip-Flop Path?
        • Why Does Copper at 1 GHz Carry Current in Only a 2 µm Layer?
        • How Do You Find Thevenin Resistance With No Independent Source?
        • How Do You Find a Load's Reflection Coefficient From Vmax and Vmin?
        • Why Can the Same Z-Transform Belong to Two Different Signals?
        • Fourier Series for GATE Signals and Systems
        • GATE ECE Preparation: A Subject-by-Subject Study Order
        • Network Theory Formulas to Know for GATE EC and EE
        • PN Junction Diode for GATE: Concepts and Common Mistakes
        • Thevenin and Norton Theorems for GATE, with Solved Examples
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Home›Explainers›#number-theory

Resources tagged “number-theory”

5 resources.

Divisibility Rules

Quick tests to check whether a number is divisible by 2 through 12, with worked examples.

Squares and Cubes Reference

Squares from 1 to 30 and cubes from 1 to 20, with last-digit patterns, mental squaring shortcuts, and how to find square and cube roots of perfect powers.

Real Numbers: HCF and LCM

Finding HCF using Euclid's division algorithm and prime factorization, plus verifying LCM x HCF = product of two numbers, with worked examples.

Real Numbers: Irrational Numbers and Decimal Expansions

Proving a number is irrational by contradiction, and telling whether a fraction has a terminating or repeating decimal expansion, with worked examples.

Prime Numbers

Prime numbers up to 100, why 0 and 1 aren't prime, checking primality up to the square root, prime factorization and distinct prime factors, twin and co-primes, and common mistakes.

All pages in this section
  • GATE ECE
    • Subjects
      • Networks
      • Electronic Devices
    • Past papers
      • GATE 2026 paper
      • GATE 2025 paper
      • GATE 2024 paper
      • GATE 2023 paper
    • Questions by topic
      • General Aptitude
      • Engineering Mathematics
      • Networks, Signals and Systems
      • Electronic Devices
      • Analog Circuits
      • Digital Circuits
      • Control Systems
      • Communications
      • Electromagnetics
    • Formula sheets
      • Engineering Mathematics
      • Networks
      • Signals and Systems
      • Electronic Devices
      • Analog Circuits
      • Digital Circuits
      • Control Systems
      • Communications
      • Electromagnetics
  • GATE 2027
    • GATE 2027 countdown
    • GATE score calculator
    • Practice calculator for GATE
    • dB conversion calculator
    • VSWR and return loss calculator
    • Skin depth calculator
    • RC and RL time constant calculator
    • Diode small-signal resistance calculator
  • Explainers
    • Math: Calculus
      • Chain Rule
      • Definite Integrals
      • Power Rule
      • Product Rule
      • Quotient Rule
      • Applications of Derivatives
      • Implicit Differentiation
      • Increasing and Decreasing Functions
      • Maxima and Minima
      • Rolle's Theorem
      • Tangents and Normals
      • Integration by Partial Fractions
      • Integration of Particular Functions
      • Integration Using Trigonometric Identities
      • Integral of e^x[f(x) + f'(x)]
      • Finding the Area Bounded by a Curve
      • Differential Equations
      • Integration by Parts
      • Continuity
      • Approximations Using Differentials
      • Linear Programming
    • Math: Vectors and 3D Geometry
      • Operations on Vectors
      • Finding a Unit Vector
      • Projection of a Vector
      • Finding the Position Vector of a Point
      • Finding Direction Cosines
      • Finding the Equation of a Line
      • Equation of a Plane
      • Angle Between a Line and a Plane
      • Shortest Distance Between Two Lines
      • Area of a Triangle and Parallelogram Using Vectors
    • Math: Algebra
      • Quadratic Equations
      • Arithmetic Progressions
      • Probability
      • Logarithms
      • Complex Numbers
      • Permutations and Combinations
      • Laws of Exponents
    • Math: Arithmetic and Number
      • Percentage
      • Ratio and Proportion
      • Simple and Compound Interest
      • Data Interpretation: Bar Graphs
    • Math: Matrices and Determinants
      • Operations on Matrices
      • Special Types of Matrices
      • Symmetric and Skew-Symmetric Matrices
      • Square Matrix Properties
      • Solving a System of Equations with Matrices
      • Area of a Triangle Using Determinants
    • Math: Sets, Relations and Functions
      • Types of Relations
      • Types of Functions
      • Binary Operation
      • Composition of Functions (gof and fog)
      • Operations on Sets
    • Math: Geometry and Mensuration
      • Area and Perimeter Formulas Reference
      • Surface Area and Volume Formulas Reference
    • Math: Trigonometry
      • Trigonometry Basics
      • Inverse Trigonometric Functions
      • Degrees and Radians
    • Physics
      • Engineering Units, SI Prefixes and Decibels
      • Wave Optics: Young's Double Slit Experiment
      • Diffraction: Single Slit and Diffraction Grating
      • Photoelectric Effect
      • de Broglie Wavelength and Matter Waves
    • Engineering Mathematics
      • Laplace Transforms
      • Fourier Series
      • Eigenvalues and Eigenvectors
      • Partial Differentiation
      • Vector Calculus: Gradient, Divergence, and Curl
    • Computer Science
      • Logic Gates
      • Boolean Algebra
      • Stack (Data Structure)
    • Electrical and Electronics
      • Kirchhoff's Current and Voltage Laws
      • PN Junction Diode: Forward and Reverse Bias
      • Thevenin's and Norton's Theorems
      • Transistor Biasing
      • Op-Amp Fundamentals: Inverting and Non-Inverting Amplifiers
    • Blog
      • JEE Main and Advanced
        • JEE Main Marking Scheme Explained: The Current Pattern and How It Got Here
        • JEE Main Percentile, NTA Score and Rank: How Normalization Actually Works
        • JEE Main Eligibility: Age Limit, Number of Attempts, and the 75% Rule Explained
        • 8 Things to Check on Your JEE Main Admit Card Before Exam Day
        • How Many Physics Numericals You Actually Need to Solve Before JEE Main
        • JEE Main Tie-Breaking Rules: What Actually Decides Your Rank on a Tie
        • How Many JEE Main Mock Tests You Actually Need, and When to Start
        • JEE Main vs JEE Advanced: How Your Preparation Actually Needs to Change
      • NEET UG
        • NEET UG 2027 Goes Computer-Based: What Actually Changes (and How to Prepare)
        • 12 NEET High-Weightage Chapters to Prioritize When Time Is Short
        • Is NCERT Enough for NEET? What the Marks Split Actually Tells You
        • NEET Negative Marking: When Guessing Is Actually Worth It
      • Counselling and Admissions
        • No Seat in JoSAA Round 1, Round 2, or the Final Round? Here's What Happens Next
        • NEET All India Rank vs State Rank: Which One Decides Your Seat
        • JoSAA vs CSAB: How JEE Counselling Actually Works
      • Study Plans and Exam Strategy
        • A 90-Day GATE Study Plan You Can Actually Follow
        • The Last 30 Days Before GATE: A Revision Plan
        • Common Mistakes in GATE NAT Questions
        • GATE Preparation While Working Full Time
        • Introducing Crumb: A Daily Term-Guessing Game for NEET, JEE, CLAT and More
        • 6 JEE/NEET Myths That Are Actually Wrong (or Just Outdated)
        • Should You Drop a Year for JEE/NEET? A Framework, Not a Feeling
        • 4 Silly Mistakes Costing You Marks in JEE/NEET (and How to Fix Each One)
        • How to Revise Your Entire JEE/NEET Syllabus in the Last 30 Days
        • 5 Rules for a JEE/NEET Study Timetable That Doesn't Burn You Out
      • ECE Topics
        • How Far Does the Fermi Level Move When You Dope Silicon?
        • How Many Flip-Flops Does a Mod-N Counter Need?
        • Why Does a Zener Diode Hold Its Voltage, and When Does It Stop?
        • Why Can't AM Put More Than a Third of Its Power in the Sidebands?
        • How Does a Diode's Small-Signal Resistance Change With Bias Current?
        • Why Does the Early Effect Give a BJT a Finite Output Resistance?
        • Why Does a Fourier Series Overshoot by 9% at Every Jump?
        • How Does a Hamming (7,4) Syndrome Point to the Flipped Bit?
        • What Do Students Get Wrong About Don't-Cares in K-Maps?
        • How Much Does the Miller Effect Cut Common-Emitter Bandwidth?
        • How Does the Nyquist Criterion Handle a Pole on the jω Axis?
        • Why Does an Op-Amp Integrator Saturate, and How Long Does It Take?
        • What Do You Do When a Routh Array Has a Zero in the First Column?
        • Why Does Resistance Lower Q in Series RLC but Raise It in Parallel?
        • How Do You Calculate Setup and Hold Slack for a Flip-Flop Path?
        • Why Does Copper at 1 GHz Carry Current in Only a 2 µm Layer?
        • How Do You Find Thevenin Resistance With No Independent Source?
        • How Do You Find a Load's Reflection Coefficient From Vmax and Vmin?
        • Why Can the Same Z-Transform Belong to Two Different Signals?
        • Fourier Series for GATE Signals and Systems
        • GATE ECE Preparation: A Subject-by-Subject Study Order
        • Network Theory Formulas to Know for GATE EC and EE
        • PN Junction Diode for GATE: Concepts and Common Mistakes
        • Thevenin and Norton Theorems for GATE, with Solved Examples
      • GATE 2027 Guides
        • How to Check Your GATE 2027 Response Sheet Against the Answer Key
        • How Do You Enter Answers and Use the Virtual Calculator in GATE?
        • GATE 2027 Eligibility, Explained with Official Links
        • GATE 2027 Exam Date and Schedule: Every Official Date So Far
        • GATE 2027 Syllabus: Where to Find Your Branch's Official Syllabus
        • How the GATE Application Process Works: Documents to Exam Day
        • GATE CS Preparation: A Subject-by-Subject Study Order
        • GATE Marking Scheme: MCQ, MSQ, NAT and Negative Marking
        • GATE Score vs Marks: How Your GATE Score Is Calculated
        • How GATE Normalization Works Across Multiple Sessions
      • College, Careers and Other Exams
        • 5 Tips for a GMAT Study Plan While Working Full-Time
        • What a Pre-Placement Offer (PPO) Means, and How to Decide Whether to Take It
        • What to Expect in 1st-Year Engineering After JEE

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