Free · Class 10 · 6 worksheets · answer keys · practise online · set 34
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 34
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1090 Prime factorisation of 935 Prime factorisation of 2110 Prime factorisation of 1251 Prime factorisation of 147 Prime factorisation of 1475 Prime factorisation of 2584 Prime factorisation of 1078 Prime factorisation of 2200 Prime factorisation of 1813
✅ Answer key — Prime factorisation
2 × 5 × 109 5 × 11 × 17 2 × 5 × 211 3² × 139 3 × 7² 5² × 59 2³ × 17 × 19 2 × 7² × 11 2³ × 5² × 11 7² × 37 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 34
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 88 and 121 HCF and LCM of 99 and 135 HCF and LCM of 126 and 162 HCF and LCM of 38 and 57 HCF and LCM of 54 and 144 HCF and LCM of 64 and 104 HCF and LCM of 21 and 24 HCF and LCM of 51 and 238
✅ Answer key — HCF and LCM
HCF = 11, LCM = 968 HCF = 9, LCM = 1485 HCF = 18, LCM = 1134 HCF = 19, LCM = 114 HCF = 18, LCM = 432 HCF = 8, LCM = 832 HCF = 3, LCM = 168 HCF = 17, LCM = 714 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 34
Name: Date: Score: / 8
Find the HCF.
HCF of 374 and 198 (Euclid’s division algorithm) HCF of 276 and 168 (Euclid’s division algorithm) HCF of 696 and 144 (Euclid’s division algorithm) HCF of 275 and 264 (Euclid’s division algorithm) HCF of 987 and 483 (Euclid’s division algorithm) HCF of 708 and 180 (Euclid’s division algorithm) HCF of 273 and 231 (Euclid’s division algorithm) HCF of 448 and 126 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
22 12 24 11 21 12 21 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 34
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 700. One number is 70. Find the other. HCF of two numbers is 14 and their LCM is 1540. One number is 140. Find the other. HCF of two numbers is 8 and their LCM is 160. One number is 32. Find the other. HCF of two numbers is 12 and their LCM is 720. One number is 144. Find the other. HCF of two numbers is 12 and their LCM is 240. One number is 60. Find the other. HCF of two numbers is 11 and their LCM is 1089. One number is 121. Find the other.
✅ Answer key — HCF × LCM = product
100 154 40 60 48 99 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 34
Name: Date: Score: / 8
Answer without long division.
Does 11/4 have a terminating decimal expansion? Does 13/80 have a terminating decimal expansion? Does 13/5 have a terminating decimal expansion? Does 5/6 have a terminating decimal expansion? Does 39/20 have a terminating decimal expansion? Does 2019/2000 have a terminating decimal expansion? Does 6/5 have a terminating decimal expansion? Does 4569/2000 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2²) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 5) Yes — terminating (denominator 2⁴ × 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 34
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9√67 Rational or irrational: 6√66 Rational or irrational: √23 Rational or irrational: √76 Rational or irrational: 5√6 Rational or irrational: √97 Rational or irrational: 9√58 Rational or irrational: 2√3 Rational or irrational: 3 + √43 Rational or irrational: 9√47 Rational or irrational: √98 Rational or irrational: √39
✅ 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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