Free · Class 10 · 6 worksheets · answer keys · practise online · set 23
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 23
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2726 Prime factorisation of 796 Prime factorisation of 1640 Prime factorisation of 2040 Prime factorisation of 963 Prime factorisation of 568 Prime factorisation of 1566 Prime factorisation of 2337 Prime factorisation of 2783 Prime factorisation of 2852
✅ Answer key — Prime factorisation
2 × 29 × 47 2² × 199 2³ × 5 × 41 2³ × 3 × 5 × 17 3² × 107 2³ × 71 2 × 3³ × 29 3 × 19 × 41 11² × 23 2² × 23 × 31 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 23
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 30 and 66 HCF and LCM of 78 and 84 HCF and LCM of 24 and 52 HCF and LCM of 75 and 165 HCF and LCM of 30 and 165 HCF and LCM of 15 and 65 HCF and LCM of 56 and 80 HCF and LCM of 99 and 121
✅ Answer key — HCF and LCM
HCF = 6, LCM = 330 HCF = 6, LCM = 1092 HCF = 4, LCM = 312 HCF = 15, LCM = 825 HCF = 15, LCM = 330 HCF = 5, LCM = 195 HCF = 8, LCM = 560 HCF = 11, LCM = 1089 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 23
Name: Date: Score: / 8
Find the HCF.
HCF of 531 and 108 (Euclid’s division algorithm) HCF of 392 and 189 (Euclid’s division algorithm) HCF of 444 and 432 (Euclid’s division algorithm) HCF of 480 and 345 (Euclid’s division algorithm) HCF of 875 and 675 (Euclid’s division algorithm) HCF of 600 and 210 (Euclid’s division algorithm) HCF of 851 and 322 (Euclid’s division algorithm) HCF of 450 and 280 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
9 7 12 15 25 30 23 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 23
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 36. One number is 9. Find the other. HCF of two numbers is 2 and their LCM is 20. One number is 4. Find the other. HCF of two numbers is 13 and their LCM is 455. One number is 91. Find the other. HCF of two numbers is 6 and their LCM is 792. One number is 66. Find the other. HCF of two numbers is 15 and their LCM is 1650. One number is 165. Find the other. HCF of two numbers is 4 and their LCM is 40. One number is 8. Find the other.
✅ Answer key — HCF × LCM = product
12 10 65 72 150 20 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 23
Name: Date: Score: / 8
Answer without long division.
Does 511/176 have a terminating decimal expansion? Does 361/400 have a terminating decimal expansion? Does 111/50 have a terminating decimal expansion? Does 226/125 have a terminating decimal expansion? Does 61/24 have a terminating decimal expansion? Does 57/25 have a terminating decimal expansion? Does 145/88 have a terminating decimal expansion? Does 747/625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 11) 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 23
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 5 + √54 Rational or irrational: √88 Rational or irrational: 2√54 Rational or irrational: √60 Rational or irrational: 2√75 Rational or irrational: √4 Rational or irrational: 8 + √61 Rational or irrational: 7 + √46 Rational or irrational: 4 + √53 Rational or irrational: 3√47 Rational or irrational: √80 Rational or irrational: 7√83
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational rational 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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