Free · Class 10 · 6 worksheets · answer keys · practise online · set 85
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 85
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1000 Prime factorisation of 693 Prime factorisation of 1392 Prime factorisation of 2769 Prime factorisation of 1104 Prime factorisation of 2817 Prime factorisation of 1323 Prime factorisation of 628 Prime factorisation of 584 Prime factorisation of 556
✅ Answer key — Prime factorisation
2³ × 5³ 3² × 7 × 11 2⁴ × 3 × 29 3 × 13 × 71 2⁴ × 3 × 23 3² × 313 3³ × 7² 2² × 157 2³ × 73 2² × 139 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 85
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 40 and 90 HCF and LCM of 24 and 60 HCF and LCM of 18 and 27 HCF and LCM of 45 and 150 HCF and LCM of 54 and 63 HCF and LCM of 40 and 150 HCF and LCM of 65 and 182 HCF and LCM of 54 and 117
✅ Answer key — HCF and LCM
HCF = 10, LCM = 360 HCF = 12, LCM = 120 HCF = 9, LCM = 54 HCF = 15, LCM = 450 HCF = 9, LCM = 378 HCF = 10, LCM = 600 HCF = 13, LCM = 910 HCF = 9, LCM = 702 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 85
Name: Date: Score: / 8
Find the HCF.
HCF of 800 and 725 (Euclid’s division algorithm) HCF of 464 and 184 (Euclid’s division algorithm) HCF of 486 and 153 (Euclid’s division algorithm) HCF of 588 and 564 (Euclid’s division algorithm) HCF of 304 and 232 (Euclid’s division algorithm) HCF of 440 and 136 (Euclid’s division algorithm) HCF of 900 and 640 (Euclid’s division algorithm) HCF of 686 and 266 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
25 8 9 12 8 8 20 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 85
Name: Date: Score: / 6
Solve.
HCF of two numbers is 12 and their LCM is 480. One number is 96. Find the other. HCF of two numbers is 4 and their LCM is 176. One number is 44. Find the other. HCF of two numbers is 7 and their LCM is 588. One number is 49. Find the other. HCF of two numbers is 6 and their LCM is 594. One number is 66. Find the other. HCF of two numbers is 11 and their LCM is 385. One number is 55. Find the other. HCF of two numbers is 12 and their LCM is 840. One number is 84. Find the other.
✅ Answer key — HCF × LCM = product
60 16 84 54 77 120 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 85
Name: Date: Score: / 8
Answer without long division.
Does 123/625 have a terminating decimal expansion? Does 1561/550 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 31/22 have a terminating decimal expansion? Does 381/176 have a terminating decimal expansion? Does 667/280 have a terminating decimal expansion? Does 12/5 have a terminating decimal expansion? Does 53/104 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 13) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 85
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 4√97 Rational or irrational: √42 Rational or irrational: √26 Rational or irrational: 1 + √14 Rational or irrational: √8 Rational or irrational: √75 Rational or irrational: 3 + √27 Rational or irrational: 4 + √47 Rational or irrational: 8√81 Rational or irrational: 2√84 Rational or irrational: √60 Rational or irrational: 6√45
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational rational 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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