Fundamental Theorem of Arithmetic
Every composite number can be uniquely expressed as a product of prime powers, apart from the order of factors.
Grade 10th · Mathematics · Real Numbers
Real Numbers, Fundamental Theorem of Arithmetic & HCF/LCM
Master Real Numbers, Fundamental Theorem of Arithmetic & HCF/LCM for Grade 10th Mathematics. Includes verified formulas, core concepts, step-by-step checklists, and interactive solver tools.
Science StreamFundamental Level
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Essential Formulas & Mathematical Definitions
HCF(a, b) × LCM(a, b) = a × b
a = bq + r (0 ≤ r < b)
Proof of Irrationality (Contradiction Method)
Assume √p is rational (a/b coprime). Squaring leads to common factor p dividing both a and b, contradicting the coprime assumption.
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Exam Day Revision & Problem Solving Checklist
- ✓Verify HCF × LCM = a × b product formula
- ✓Check denominator prime factors 2ⁿ 5ᵐ for terminating decimal expansion
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High-Yield Exam Strategy & Scoring Tips
Step-by-Step Mark Allocation
Always state the governing principle or formula first, write given values with standard SI units, substitute clearly, and highlight the final numerical answer with units in a box for full step marking.
Common Calculation Traps
Watch for unit prefixes (cm to m, minutes to seconds, g to kg, degrees to radians). In coordinate and ray optics problems, double-check Cartesian sign conventions before computing.
Recommended Practice & Calculation Tools
Test your understanding and perform instant calculations with these free online utilities.
Statistics & Probability Data Analyzer
Compute descriptive statistics (mean, median, mode, standard deviation, variance) from raw comma-separated datasets.
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Frequently Asked Exam Questions & Concept Clarifications
Can HCF × LCM = a × b × c be used for 3 numbers?
No. The product formula HCF × LCM = a × b applies strictly to pairs of numbers, not triplets.