Free · Class 10 · 6 worksheets · answer keys · practise online · set 69
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 69
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1680 Prime factorisation of 786 Prime factorisation of 1816 Prime factorisation of 2976 Prime factorisation of 2000 Prime factorisation of 255 Prime factorisation of 470 Prime factorisation of 2470 Prime factorisation of 1012 Prime factorisation of 2514
✅ Answer key — Prime factorisation
2⁴ × 3 × 5 × 7 2 × 3 × 131 2³ × 227 2⁵ × 3 × 31 2⁴ × 5³ 3 × 5 × 17 2 × 5 × 47 2 × 5 × 13 × 19 2² × 11 × 23 2 × 3 × 419 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF and LCM Class 10 · Worksheet 2 · set 69
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 140 and 150 HCF and LCM of 64 and 208 HCF and LCM of 27 and 126 HCF and LCM of 198 and 234 HCF and LCM of 12 and 28 HCF and LCM of 9 and 24 HCF and LCM of 24 and 30 HCF and LCM of 99 and 108
✅ Answer key — HCF and LCM
HCF = 10, LCM = 2100 HCF = 16, LCM = 832 HCF = 9, LCM = 378 HCF = 18, LCM = 2574 HCF = 4, LCM = 84 HCF = 3, LCM = 72 HCF = 6, LCM = 120 HCF = 9, LCM = 1188 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 69
Name: Date: Score: / 8
Find the HCF.
HCF of 740 and 100 (Euclid’s division algorithm) HCF of 333 and 297 (Euclid’s division algorithm) HCF of 510 and 270 (Euclid’s division algorithm) HCF of 615 and 510 (Euclid’s division algorithm) HCF of 344 and 288 (Euclid’s division algorithm) HCF of 399 and 112 (Euclid’s division algorithm) HCF of 336 and 200 (Euclid’s division algorithm) HCF of 270 and 186 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
20 9 30 15 8 7 8 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
HCF × LCM = product Class 10 · Worksheet 4 · set 69
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 60. One number is 20. Find the other. HCF of two numbers is 4 and their LCM is 112. One number is 16. Find the other. HCF of two numbers is 13 and their LCM is 572. One number is 52. Find the other. HCF of two numbers is 14 and their LCM is 420. One number is 70. Find the other. HCF of two numbers is 4 and their LCM is 288. One number is 36. Find the other. HCF of two numbers is 5 and their LCM is 300. One number is 25. Find the other.
✅ Answer key — HCF × LCM = product
30 28 143 84 32 60 TalentJR · talentjr.in/real-numbers-class-10-worksheet
🖨️ Print / save as PDF
✅ Show answers
▶️ Practise online
Terminating decimals Class 10 · Worksheet 5 · set 69
Name: Date: Score: / 8
Answer without long division.
Does 19/10 have a terminating decimal expansion? Does 158/625 have a terminating decimal expansion? Does 8/5 have a terminating decimal expansion? Does 41/75 have a terminating decimal expansion? Does 11/8 have a terminating decimal expansion? Does 107/100 have a terminating decimal expansion? Does 7/5 have a terminating decimal expansion? Does 4/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2³) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 5) Yes — terminating (denominator 5) 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 69
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 1√43 Rational or irrational: 7√89 Rational or irrational: √96 Rational or irrational: 3 + √2 Rational or irrational: 8 + √80 Rational or irrational: √69 Rational or irrational: 7√48 Rational or irrational: √9 Rational or irrational: √88 Rational or irrational: √11 Rational or irrational: 1√42 Rational or irrational: 7√25
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational rational irrational irrational irrational rational 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.
