Free · Class 10 · 6 worksheets · answer keys · practise online · set 77
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 77
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1917 Prime factorisation of 2235 Prime factorisation of 2808 Prime factorisation of 2114 Prime factorisation of 153 Prime factorisation of 2422 Prime factorisation of 2891 Prime factorisation of 343 Prime factorisation of 539 Prime factorisation of 1160
✅ Answer key — Prime factorisation
3³ × 71 3 × 5 × 149 2³ × 3³ × 13 2 × 7 × 151 3² × 17 2 × 7 × 173 7² × 59 7³ 7² × 11 2³ × 5 × 29 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 77
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 187 and 221 HCF and LCM of 72 and 112 HCF and LCM of 154 and 210 HCF and LCM of 24 and 80 HCF and LCM of 42 and 66 HCF and LCM of 18 and 45 HCF and LCM of 81 and 126 HCF and LCM of 80 and 88
✅ Answer key — HCF and LCM
HCF = 17, LCM = 2431 HCF = 8, LCM = 1008 HCF = 14, LCM = 2310 HCF = 8, LCM = 240 HCF = 6, LCM = 462 HCF = 9, LCM = 90 HCF = 9, LCM = 1134 HCF = 8, LCM = 880 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 77
Name: Date: Score: / 8
Find the HCF.
HCF of 918 and 374 (Euclid’s division algorithm) HCF of 560 and 530 (Euclid’s division algorithm) HCF of 918 and 289 (Euclid’s division algorithm) HCF of 696 and 408 (Euclid’s division algorithm) HCF of 841 and 116 (Euclid’s division algorithm) HCF of 148 and 111 (Euclid’s division algorithm) HCF of 275 and 121 (Euclid’s division algorithm) HCF of 885 and 360 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
34 10 17 24 29 37 11 15 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 77
Name: Date: Score: / 6
Solve.
HCF of two numbers is 7 and their LCM is 539. One number is 77. Find the other. HCF of two numbers is 2 and their LCM is 66. One number is 6. Find the other. HCF of two numbers is 11 and their LCM is 110. One number is 22. Find the other. HCF of two numbers is 6 and their LCM is 462. One number is 66. Find the other. HCF of two numbers is 4 and their LCM is 168. One number is 24. Find the other. HCF of two numbers is 10 and their LCM is 660. One number is 60. Find the other.
✅ Answer key — HCF × LCM = product
49 22 55 42 28 110 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 77
Name: Date: Score: / 8
Answer without long division.
Does 36/35 have a terminating decimal expansion? Does 41/56 have a terminating decimal expansion? Does 73/80 have a terminating decimal expansion? Does 73/40 have a terminating decimal expansion? Does 2243/750 have a terminating decimal expansion? Does 2809/1000 have a terminating decimal expansion? Does 9/5 have a terminating decimal expansion? Does 123/44 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 11) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 77
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9 + √45 Rational or irrational: 9√84 Rational or irrational: 3 + √49 Rational or irrational: 8 + √15 Rational or irrational: 7 + √97 Rational or irrational: 7 + √88 Rational or irrational: 8√30 Rational or irrational: √11 Rational or irrational: √68 Rational or irrational: √10 Rational or irrational: 7 + √68 Rational or irrational: 6 + √76
✅ Answer key — Rational or irrational?
irrational irrational rational 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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