NCERT Mathematics, Class 10, textbook pages 1–9

How to help your child with Class 10 Maths Chapter 1, Real Numbers, at home

Fundamental Theorem of Arithmetic and irrationality, explained for parents: a 45-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

140 = 2² × 5 × 7unique prime factorisation√2 is irrational

NCERT Class 10 Maths Chapter 1 Real Numbers: what it teaches

Every composite number is a unique product of primes. Your teen uses prime factorisation to find HCF and LCM, and proves numbers like √2, √3 and √5 are irrational.

Why it matters later. Proof techniques and factorisation return in polynomials and Class 11 reasoning.

See it: this chapter in pictures

96 = 2⁵ × 3404 = 2² × 101HCF 4, LCM 9696
Lowest powers for HCF, highest for LCM.
assume √2 = p/q (lowest terms)p² = 2q² → p, q both evencontradiction!
Proof by contradiction.
HCF × LCM= product of two numbers6 & 20: 2 × 60 = 120 ✓
Works for two numbers only.

You need

  • a factor-tree worksheet
  • a calculator for checking

Tonight’s 45 minutes

  1. Factorise 140 and 156 into primes.
  2. Find HCF and LCM of 96 and 404 by prime factorisation.
  3. Check HCF × LCM = product for two numbers.
  4. Walk through the proof that √2 is irrational, then ask your teen to write the √3 proof.

Words to use

  • prime factorisation
  • HCF
  • LCM
  • irrational
  • proof by contradiction

Watch for

  • Using HCF × LCM = product for three numbers. It works only for two numbers.
  • Proof steps skipped. Write each assumption and why it leads to a contradiction.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouWhy is √2 irrational?

Your childIf √2 = p/q, then p² = 2q², so p is even… and q too. Contradiction.

A game for this week: Factor tree race

  1. Call a 3-digit number.
  2. Race to its prime factorisation.
  3. Check by multiplying.
  4. Fastest correct wins.

A 5-day plan, 45 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Scheduling repeating events (LCM).
  • Cutting materials evenly (HCF).
  • Encryption uses primes.
  • Measurement with irrational lengths.

Quick check

Ask these at the end of the week. Tap to see the answer.

Prime factorisation of 140?

2² × 5 × 7.

HCF and LCM of 6 and 20?

2 and 60.

Is 5 − √3 rational?

No, irrational.

Ready for the next chapter when your child…

  • Factorises into primes confidently.
  • Finds HCF and LCM by factorisation.
  • Writes a proof of irrationality.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 10). See the full Class 10 parent guide for every chapter.

Questions parents ask

What is the Fundamental Theorem of Arithmetic?

Every composite number has a unique prime factorisation.

How do I prove √2 is irrational?

Assume √2 = p/q in lowest terms and show p and q are both even, a contradiction.

Is Euclid’s division lemma in the syllabus?

The current book focuses on the Fundamental Theorem and irrationality.