Prime Factors, HCF & LCM

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

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Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

So 2, 3, 5, 7, 11 are prime. 1 is not prime (only one factor), and 2 is the only even prime.

This is the Fundamental Theorem of Arithmetic. Use a factor tree or repeated division: 84 = 2^2 x 3 x 7.

Multiply only the shared primes, each at its lower power. HCF(36, 48) = 2^2 x 3 = 12. Useful for simplifying fractions.

Take every prime at its higher power. LCM(36, 48) = 2^4 x 3^2 = 144. Useful for common denominators and 'when next together' problems.

Prime number	A whole number greater than 1 with exactly two factors: 1 and itself.
Composite number	A whole number greater than 1 with more than two factors.
Prime factorisation	Writing a number as a product of primes, usually in index form.
Factor tree	A branching diagram that splits a number until all branches are prime.
HCF	Highest Common Factor: the largest number dividing two numbers exactly.
LCM	Lowest Common Multiple: the smallest number that is a multiple of both.
Index notation	Showing repeated multiplication as a base and power, e.g. 2x2x2 = 2^3.
Venn diagram	Overlapping circles showing shared and unshared factors.

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