Free · Class 10 · 6 worksheets · answer keys · practise online · set 80
Real numbers worksheets — Class 10, with answers
Free real numbers Class 10 worksheets (Chapter 1): prime factorisation, HCF and LCM, Euclid’s division algorithm, HCF × LCM, terminating decimals and irrational numbers — with answers.
💡 Learn it first
Fundamental theorem of arithmetic : every composite number is a product of primes in exactly one way: 360 = 2³ × 3² × 5.HCF = product of the smallest powers of common primes; LCM = product of the greatest powers of all primes. For two numbers, HCF × LCM = product of the numbers .Euclid’s division : a = bq + r. Keep dividing the divisor by the remainder; the last non-zero remainder is the HCF.p/q (lowest terms) has a terminating decimal only if q = 2ᵐ × 5ⁿ. √2, √3, √5, 3 + √2 are irrational ; √16 = 4 is rational.
Prime factorisation (Class 10) HCF and LCM (Class 10) Euclid’s division algorithm (Class 10) HCF × LCM = product (Class 10) Terminating decimals (Class 10) Rational or irrational? (Class 9–10)
Prime factorisation Class 10 · Worksheet 1 · set 80
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 276 Prime factorisation of 1311 Prime factorisation of 1053 Prime factorisation of 576 Prime factorisation of 1426 Prime factorisation of 376 Prime factorisation of 1792 Prime factorisation of 2375 Prime factorisation of 2520 Prime factorisation of 1833
✅ Answer key — Prime factorisation
2² × 3 × 23 3 × 19 × 23 3⁴ × 13 2⁶ × 3² 2 × 23 × 31 2³ × 47 2⁸ × 7 5³ × 19 2³ × 3² × 5 × 7 3 × 13 × 47 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 80
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 90 and 234 HCF and LCM of 27 and 30 HCF and LCM of 30 and 225 HCF and LCM of 8 and 20 HCF and LCM of 12 and 22 HCF and LCM of 88 and 143 HCF and LCM of 75 and 180 HCF and LCM of 20 and 75
✅ Answer key — HCF and LCM
HCF = 18, LCM = 1170 HCF = 3, LCM = 270 HCF = 15, LCM = 450 HCF = 4, LCM = 40 HCF = 2, LCM = 132 HCF = 11, LCM = 1144 HCF = 15, LCM = 900 HCF = 5, LCM = 300 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Euclid’s division algorithm Class 10 · Worksheet 3 · set 80
Name: Date: Score: / 8
Find the HCF.
HCF of 465 and 315 (Euclid’s division algorithm) HCF of 414 and 369 (Euclid’s division algorithm) HCF of 495 and 363 (Euclid’s division algorithm) HCF of 470 and 450 (Euclid’s division algorithm) HCF of 400 and 290 (Euclid’s division algorithm) HCF of 464 and 176 (Euclid’s division algorithm) HCF of 282 and 204 (Euclid’s division algorithm) HCF of 406 and 315 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
15 9 33 10 10 16 6 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 80
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 270. One number is 45. Find the other. HCF of two numbers is 9 and their LCM is 126. One number is 18. Find the other. HCF of two numbers is 10 and their LCM is 60. One number is 20. Find the other. HCF of two numbers is 7 and their LCM is 210. One number is 42. Find the other. HCF of two numbers is 12 and their LCM is 504. One number is 72. Find the other. HCF of two numbers is 9 and their LCM is 162. One number is 81. Find the other.
✅ Answer key — HCF × LCM = product
54 63 30 35 84 18 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 80
Name: Date: Score: / 8
Answer without long division.
Does 5/2 have a terminating decimal expansion? Does 61/25 have a terminating decimal expansion? Does 4/5 have a terminating decimal expansion? Does 107/40 have a terminating decimal expansion? Does 119/50 have a terminating decimal expansion? Does 548/375 have a terminating decimal expansion? Does 373/250 have a terminating decimal expansion? Does 287/100 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) Yes — terminating (denominator 5²) Yes — terminating (denominator 5) Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2² × 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Rational or irrational? Class 9–10 · Worksheet 6 · set 80
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9 + √38 Rational or irrational: 8√44 Rational or irrational: √76 Rational or irrational: 9 + √2 Rational or irrational: √83 Rational or irrational: 8√96 Rational or irrational: √36 Rational or irrational: 9 + √51 Rational or irrational: 3√93 Rational or irrational: √74 Rational or irrational: 1√95 Rational or irrational: √45
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational rational irrational irrational irrational irrational irrational TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Questions
What is the relation between HCF and LCM? For two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.
Are these worksheets free? Yes — print them or save as PDF free. Every worksheet has an answer key.
How do I get different questions? Press “🔄 New set” — the questions change (maths numbers are new every time; English sentences are shuffled).
How do I print only one worksheet? Press “🖨️ Print” on that worksheet. Tick “with answer key” if you want the answers on a second page.
Can my child do this worksheet online, like a quiz? Yes — press “▶️ Practise online” on any worksheet. The questions come one at a time with instant marking, a score at the end and a review of mistakes. No sign-in is needed.
