Free · Class 10 · 6 worksheets · answer keys · practise online · set 21
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 21
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2398 Prime factorisation of 147 Prime factorisation of 1645 Prime factorisation of 1456 Prime factorisation of 2708 Prime factorisation of 1052 Prime factorisation of 612 Prime factorisation of 448 Prime factorisation of 428 Prime factorisation of 1656
✅ Answer key — Prime factorisation
2 × 11 × 109 3 × 7² 5 × 7 × 47 2⁴ × 7 × 13 2² × 677 2² × 263 2² × 3² × 17 2⁶ × 7 2² × 107 2³ × 3² × 23 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 21
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 65 and 117 HCF and LCM of 80 and 104 HCF and LCM of 130 and 169 HCF and LCM of 140 and 260 HCF and LCM of 51 and 68 HCF and LCM of 49 and 84 HCF and LCM of 187 and 238 HCF and LCM of 40 and 90
✅ Answer key — HCF and LCM
HCF = 13, LCM = 585 HCF = 8, LCM = 1040 HCF = 13, LCM = 1690 HCF = 20, LCM = 1820 HCF = 17, LCM = 204 HCF = 7, LCM = 588 HCF = 17, LCM = 2618 HCF = 10, LCM = 360 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 21
Name: Date: Score: / 8
Find the HCF.
HCF of 874 and 855 (Euclid’s division algorithm) HCF of 126 and 102 (Euclid’s division algorithm) HCF of 928 and 128 (Euclid’s division algorithm) HCF of 864 and 160 (Euclid’s division algorithm) HCF of 342 and 288 (Euclid’s division algorithm) HCF of 424 and 376 (Euclid’s division algorithm) HCF of 288 and 117 (Euclid’s division algorithm) HCF of 464 and 416 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
19 6 32 32 18 8 9 16 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 21
Name: Date: Score: / 6
Solve.
HCF of two numbers is 12 and their LCM is 1584. One number is 132. Find the other. HCF of two numbers is 13 and their LCM is 78. One number is 26. Find the other. HCF of two numbers is 5 and their LCM is 200. One number is 25. Find the other. HCF of two numbers is 9 and their LCM is 270. One number is 45. Find the other. HCF of two numbers is 12 and their LCM is 864. One number is 96. Find the other. HCF of two numbers is 6 and their LCM is 330. One number is 30. Find the other.
✅ Answer key — HCF × LCM = product
144 39 40 54 108 66 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 21
Name: Date: Score: / 8
Answer without long division.
Does 243/500 have a terminating decimal expansion? Does 1478/875 have a terminating decimal expansion? Does 169/100 have a terminating decimal expansion? Does 179/60 have a terminating decimal expansion? Does 3329/1375 have a terminating decimal expansion? Does 15/8 have a terminating decimal expansion? Does 79/130 have a terminating decimal expansion? Does 33/25 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 21
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √34 Rational or irrational: 4√53 Rational or irrational: 6 + √43 Rational or irrational: √99 Rational or irrational: 8 + √59 Rational or irrational: 7 + √50 Rational or irrational: 6√57 Rational or irrational: 6√86 Rational or irrational: 7 + √100 Rational or irrational: 7√73 Rational or irrational: 3√82 Rational or irrational: 2 + √14
✅ 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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