Real Numbers
Class 10 · Mathematics
3 ideas in Class 10 Mathematics, explained in plain words, with games and quizzes to practise.
Prime Factorisation and the Fundamental Theorem
Part of: Prime Factorisation and the Fundamental Theorem
Every composite positive integer has a prime factorisation that is unique apart from the order of its factors.
Why it matters. Prime factors reveal divisibility and help explain number patterns and irrationality.
Try it in two minutes
- Break a number into prime factors.
- Use shared and greatest prime powers for HCF and LCM.
- For an irrationality proof, test what follows from assuming a rational form.
Try at home. Choose two small composite numbers and write each as a product of primes, then compare their common factors.
HCF, LCM and Divisibility
Part of: HCF, LCM and Divisibility
Prime factorisation gives HCF by multiplying common primes with their smallest powers and LCM by using every prime with its greatest power.
Why it matters. Prime factors reveal divisibility and help explain number patterns and irrationality.
Try it in two minutes
- Break a number into prime factors.
- Use shared and greatest prime powers for HCF and LCM.
- For an irrationality proof, test what follows from assuming a rational form.
Try at home. Choose two small composite numbers and write each as a product of primes, then compare their common factors.
Irrational Numbers and Proofs
Part of: Irrational Numbers and Proofs
An irrational number cannot be written as a ratio of integers with nonzero denominator. Contradiction proofs use prime divisibility to rule out a rational form for square roots of primes.
Why it matters. Prime factors reveal divisibility and help explain number patterns and irrationality.
Try it in two minutes
- Break a number into prime factors.
- Use shared and greatest prime powers for HCF and LCM.
- For an irrationality proof, test what follows from assuming a rational form.
Try at home. Choose two small composite numbers and write each as a product of primes, then compare their common factors.
What your child will practise
- HCF, LCM and Divisibility: Desert Puzzle (Clue Puzzle)
- HCF, LCM and Divisibility: Ocean Quick Fire (Quick Fire)
- Irrational Numbers and Proofs: Jungle Quick Fire (Quick Fire)
- Irrational Numbers and Proofs: Mission Control Quest (Collect the Answer)
- Prime Factorisation and the Fundamental Theorem: Number Sort (Sort It Out)
- Quiz: HCF, LCM and Divisibility (8 questions)
- Quiz: Irrational Numbers and Proofs (8 questions)
- Quiz: Prime Factorisation and the Fundamental Theorem (8 questions)