Free · Class 10 · 6 worksheets · answer keys · practise online · set 94
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 94
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 602 Prime factorisation of 1920 Prime factorisation of 536 Prime factorisation of 2565 Prime factorisation of 1604 Prime factorisation of 2216 Prime factorisation of 640 Prime factorisation of 760 Prime factorisation of 2849 Prime factorisation of 441
✅ Answer key — Prime factorisation
2 × 7 × 43 2⁷ × 3 × 5 2³ × 67 3³ × 5 × 19 2² × 401 2³ × 277 2⁷ × 5 2³ × 5 × 19 7 × 11 × 37 3² × 7² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 94
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 65 and 182 HCF and LCM of 120 and 130 HCF and LCM of 24 and 180 HCF and LCM of 76 and 171 HCF and LCM of 6 and 39 HCF and LCM of 27 and 117 HCF and LCM of 36 and 56 HCF and LCM of 56 and 96
✅ Answer key — HCF and LCM
HCF = 13, LCM = 910 HCF = 10, LCM = 1560 HCF = 12, LCM = 360 HCF = 19, LCM = 684 HCF = 3, LCM = 78 HCF = 9, LCM = 351 HCF = 4, LCM = 504 HCF = 8, LCM = 672 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 94
Name: Date: Score: / 8
Find the HCF.
HCF of 825 and 198 (Euclid’s division algorithm) HCF of 550 and 470 (Euclid’s division algorithm) HCF of 990 and 627 (Euclid’s division algorithm) HCF of 476 and 462 (Euclid’s division algorithm) HCF of 696 and 360 (Euclid’s division algorithm) HCF of 296 and 168 (Euclid’s division algorithm) HCF of 406 and 385 (Euclid’s division algorithm) HCF of 935 and 799 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
33 10 33 14 24 8 7 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 94
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 546. One number is 91. Find the other. HCF of two numbers is 2 and their LCM is 126. One number is 18. Find the other. HCF of two numbers is 15 and their LCM is 1260. One number is 105. Find the other. HCF of two numbers is 6 and their LCM is 84. One number is 12. Find the other. HCF of two numbers is 13 and their LCM is 273. One number is 39. Find the other. HCF of two numbers is 9 and their LCM is 396. One number is 36. Find the other.
✅ Answer key — HCF × LCM = product
78 14 180 42 91 99 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 94
Name: Date: Score: / 8
Answer without long division.
Does 133/50 have a terminating decimal expansion? Does 441/220 have a terminating decimal expansion? Does 2153/1000 have a terminating decimal expansion? Does 4691/2000 have a terminating decimal expansion? Does 1357/1000 have a terminating decimal expansion? Does 294/625 have a terminating decimal expansion? Does 17/6 have a terminating decimal expansion? Does 1742/625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 94
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √66 Rational or irrational: √76 Rational or irrational: 3 + √63 Rational or irrational: 5 + √59 Rational or irrational: √64 Rational or irrational: 6 + √46 Rational or irrational: 4√10 Rational or irrational: √43 Rational or irrational: √17 Rational or irrational: √39 Rational or irrational: 7 + √45 Rational or irrational: 9√32
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational rational irrational irrational 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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