Free · Class 10 · 6 worksheets · answer keys · practise online · set 81
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 81
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1175 Prime factorisation of 288 Prime factorisation of 2524 Prime factorisation of 1794 Prime factorisation of 1698 Prime factorisation of 1512 Prime factorisation of 2940 Prime factorisation of 234 Prime factorisation of 1048 Prime factorisation of 1767
✅ Answer key — Prime factorisation
5² × 47 2⁵ × 3² 2² × 631 2 × 3 × 13 × 23 2 × 3 × 283 2³ × 3³ × 7 2² × 3 × 5 × 7² 2 × 3² × 13 2³ × 131 3 × 19 × 31 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 81
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 28 and 36 HCF and LCM of 8 and 44 HCF and LCM of 6 and 28 HCF and LCM of 42 and 49 HCF and LCM of 35 and 40 HCF and LCM of 15 and 27 HCF and LCM of 96 and 208 HCF and LCM of 70 and 112
✅ Answer key — HCF and LCM
HCF = 4, LCM = 252 HCF = 4, LCM = 88 HCF = 2, LCM = 84 HCF = 7, LCM = 294 HCF = 5, LCM = 280 HCF = 3, LCM = 135 HCF = 16, LCM = 1248 HCF = 14, LCM = 560 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 81
Name: Date: Score: / 8
Find the HCF.
HCF of 867 and 799 (Euclid’s division algorithm) HCF of 666 and 648 (Euclid’s division algorithm) HCF of 182 and 168 (Euclid’s division algorithm) HCF of 975 and 500 (Euclid’s division algorithm) HCF of 900 and 340 (Euclid’s division algorithm) HCF of 329 and 182 (Euclid’s division algorithm) HCF of 484 and 253 (Euclid’s division algorithm) HCF of 330 and 186 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
17 18 14 25 20 7 11 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 81
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 891. One number is 99. Find the other. HCF of two numbers is 13 and their LCM is 1716. One number is 143. Find the other. HCF of two numbers is 5 and their LCM is 660. One number is 55. Find the other. HCF of two numbers is 9 and their LCM is 693. One number is 99. Find the other. HCF of two numbers is 15 and their LCM is 495. One number is 165. Find the other. HCF of two numbers is 2 and their LCM is 132. One number is 12. Find the other.
✅ Answer key — HCF × LCM = product
81 156 60 63 45 22 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 81
Name: Date: Score: / 8
Answer without long division.
Does 306/625 have a terminating decimal expansion? Does 527/300 have a terminating decimal expansion? Does 41/220 have a terminating decimal expansion? Does 69/875 have a terminating decimal expansion? Does 782/625 have a terminating decimal expansion? Does 5201/1875 have a terminating decimal expansion? Does 1/24 have a terminating decimal expansion? Does 1653/625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 3) 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 81
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √80 Rational or irrational: 3 + √34 Rational or irrational: 5 + √18 Rational or irrational: 1√65 Rational or irrational: 9√74 Rational or irrational: 2√68 Rational or irrational: 9√80 Rational or irrational: √41 Rational or irrational: 6 + √42 Rational or irrational: √95 Rational or irrational: √13 Rational or irrational: 3√86
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational 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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