Real Numbers is Chapter 1 of the Class 10 board syllabus, and it sets the tone for the year: precise, rule-based, and full of marks for a student who is careful. Your child will find HCF and LCM by prime factorisation and by Euclid’s division algorithm, use the neat rule that HCF × LCM equals the product of the two numbers, decide whether a fraction’s decimal will terminate, and follow the classic proof that √2 is irrational.

This free printable worksheet has 12 questions from Bmathpro’s own question bank of 10,500+ validated maths questions — the same bank our enrolled students practise from. Every answer comes with a one-line explanation, so you can check your child’s method, not just the final answer.

Set aside 15–20 minutes, keep the answers hidden until the end, and let your child attempt every question — a wrong attempt tells you more than a skipped one.

What this worksheet covers

• HCF and LCM by prime factorisation
• Euclid’s division algorithm for HCF
• The HCF × LCM = product-of-numbers rule
• Counting prime factors in a factorisation
• Terminating vs non-terminating recurring decimals
• Telling rational and irrational numbers apart, and the proof that √2 is irrational

Maps to the CBSE Class 10 Real Numbers chapter (NCERT) and equivalent ICSE/State-board units.

Class 10 Real Numbers Worksheet — 12 Questions

Warm-up

1. Find the HCF of 12 and 18. (Write your answer.)

2. Find the LCM of 12 and 18. (Write your answer.)

3. Which of the following numbers is irrational?
A. √16  B. 0.75  C. √5  D. 22/7

Building up

4. Find the LCM of 6, 8 and 12. (Write your answer.)

5. After how many decimal places does the decimal expansion of 7/8 terminate? (Write your answer.)

6. In the prime factorisation of 60, how many prime factors are there in all (counting repeats)? (Write your answer.)

7. The proof that √2 is irrational is a proof by:
A. induction  B. direct calculation  C. contradiction  D. example

Challenge

8. Find the HCF of 96 and 404 using Euclid’s division algorithm. (Write your answer.)

9. The HCF of two numbers is 6 and their LCM is 36. If one number is 12, find the other number. (Write your answer.)

10. Which of these rational numbers has a terminating decimal expansion?
A. 23/343  B. 6/455  C. 29/64  D. 129/189

11. Two numbers have HCF 9 and LCM 360. If one number is 45, find the other. (Write your answer.)

12. The rational number 43/(2⁴ × 5³) terminates after how many decimal places? (Write your answer.)

🖨️ Print this worksheet

Answer key with explanations

Show answers and explanations (parents — open this after your child finishes)

1. 6 — 12 = 2²×3, 18 = 2×3²; HCF = 2×3 = 6.
2. 36 — LCM = 2²×3² = 36.
3. C. √5 — 5 is not a perfect square; √16 = 4, 0.75 and 22/7 are rational.
4. 24 — LCM = 2³×3 = 24.
5. 3 — 7/8 = 0.875.
6. 4 — 60 = 2×2×3×5.
7. C. contradiction — assume √2 is rational and derive a contradiction.
8. 4 — 404 = 96×4+20; 96 = 20×4+16; 20 = 16×1+4; 16 = 4×4+0.
9. 18 — product = 6×36 = 216; other = 216÷12 = 18.
10. C. 29/64 — 64 = 2⁶ (only 2s), so it terminates; the others keep a prime other than 2 or 5.
11. 72 — product = 9×360 = 3240; other = 3240÷45 = 72.
12. 4 — = 215/10000 = 0.0215.

How to use this worksheet at home

• Keep it short and calm. 15–20 minutes beats an hour of pressure.
• Write out the prime factors. “Show me 60 as a product of primes first” fixes HCF, LCM and terminating-decimal questions at once.
• Praise the method, not the marks. (We deliberately don’t put marks on our worksheets.)

FAQs

Is this worksheet free to print?
Yes — free to use and print at home, no sign-up needed.

Which syllabus does it follow?
Standard Class 10 Real Numbers chapter — CBSE (NCERT), ICSE and State boards.

How can my child tell if a fraction’s decimal will terminate without dividing it out?
Simplify the fraction, then look only at the denominator’s prime factors. Only 2s and 5s → it terminates; any other prime → non-terminating recurring. A free demo class shows it worked through.

Where can my child get more practice like this?
Enrolled students get Math Gym, our paid practice app with 10,500+ questions — see our courses page.

Also practise: Quadratic Equations · Arithmetic Progressions · all Class 10 worksheets.

Did your child enjoy these questions?

See how they do with a real teacher beside them. Book a free demo class — your child meets a Bmathpro teacher and you see how our small-batch online maths classes for Class 10 work. No fee, no obligation.

Questions? WhatsApp us: +91 89198 52512