Free · Class 10 · 6 worksheets · answer keys · practise online · set 86
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.
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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 86
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2754 Prime factorisation of 1780 Prime factorisation of 574 Prime factorisation of 104 Prime factorisation of 994 Prime factorisation of 2994 Prime factorisation of 2163 Prime factorisation of 2836 Prime factorisation of 2187 Prime factorisation of 2697
✅ Answer key — Prime factorisation
2 × 3⁴ × 17 2² × 5 × 89 2 × 7 × 41 2³ × 13 2 × 7 × 71 2 × 3 × 499 3 × 7 × 103 2² × 709 3⁷ 3 × 29 × 31 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 86
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 60 and 96 HCF and LCM of 36 and 78 HCF and LCM of 50 and 110 HCF and LCM of 66 and 77 HCF and LCM of 150 and 195 HCF and LCM of 70 and 150 HCF and LCM of 68 and 85 HCF and LCM of 77 and 88
✅ Answer key — HCF and LCM
HCF = 12, LCM = 480 HCF = 6, LCM = 468 HCF = 10, LCM = 550 HCF = 11, LCM = 462 HCF = 15, LCM = 1950 HCF = 10, LCM = 1050 HCF = 17, LCM = 340 HCF = 11, LCM = 616 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 86
Name: Date: Score: / 8
Find the HCF.
HCF of 867 and 170 (Euclid’s division algorithm) HCF of 810 and 774 (Euclid’s division algorithm) HCF of 735 and 435 (Euclid’s division algorithm) HCF of 891 and 189 (Euclid’s division algorithm) HCF of 742 and 686 (Euclid’s division algorithm) HCF of 456 and 352 (Euclid’s division algorithm) HCF of 423 and 243 (Euclid’s division algorithm) HCF of 740 and 640 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
17 18 15 27 14 8 9 20 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 86
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 264. One number is 88. Find the other. HCF of two numbers is 4 and their LCM is 84. One number is 28. Find the other. HCF of two numbers is 6 and their LCM is 198. One number is 66. Find the other. HCF of two numbers is 15 and their LCM is 150. One number is 30. Find the other. HCF of two numbers is 6 and their LCM is 462. One number is 42. Find the other. HCF of two numbers is 5 and their LCM is 90. One number is 45. Find the other.
✅ Answer key — HCF × LCM = product
24 12 18 75 66 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 86
Name: Date: Score: / 8
Answer without long division.
Does 64/55 have a terminating decimal expansion? Does 3387/1250 have a terminating decimal expansion? Does 29/16 have a terminating decimal expansion? Does 49/80 have a terminating decimal expansion? Does 89/80 have a terminating decimal expansion? Does 1/10 have a terminating decimal expansion? Does 53/25 have a terminating decimal expansion? Does 14/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 5²) Yes — terminating (denominator 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 86
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 4√18 Rational or irrational: √72 Rational or irrational: √80 Rational or irrational: √47 Rational or irrational: 7√46 Rational or irrational: 2√6 Rational or irrational: 2√100 Rational or irrational: √95 Rational or irrational: 8√91 Rational or irrational: 6 + √17 Rational or irrational: 7 + √27 Rational or irrational: √35
✅ 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
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Questions
What is the relation between HCF and LCM? For two positive integers a and b: HCF(a, b) × LCM(a, b) = a × b.
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