Free · Class 10 · 6 worksheets · answer keys · practise online · set 61
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 61
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1348 Prime factorisation of 282 Prime factorisation of 2420 Prime factorisation of 164 Prime factorisation of 2232 Prime factorisation of 2466 Prime factorisation of 1875 Prime factorisation of 135 Prime factorisation of 2046 Prime factorisation of 576
✅ Answer key — Prime factorisation
2² × 337 2 × 3 × 47 2² × 5 × 11² 2² × 41 2³ × 3² × 31 2 × 3² × 137 3 × 5⁴ 3³ × 5 2 × 3 × 11 × 31 2⁶ × 3² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 61
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 20 and 28 HCF and LCM of 30 and 40 HCF and LCM of 144 and 156 HCF and LCM of 132 and 180 HCF and LCM of 24 and 33 HCF and LCM of 55 and 143 HCF and LCM of 28 and 63 HCF and LCM of 42 and 154
✅ Answer key — HCF and LCM
HCF = 4, LCM = 140 HCF = 10, LCM = 120 HCF = 12, LCM = 1872 HCF = 12, LCM = 1980 HCF = 3, LCM = 264 HCF = 11, LCM = 715 HCF = 7, LCM = 252 HCF = 14, LCM = 462 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 61
Name: Date: Score: / 8
Find the HCF.
HCF of 510 and 360 (Euclid’s division algorithm) HCF of 624 and 533 (Euclid’s division algorithm) HCF of 187 and 102 (Euclid’s division algorithm) HCF of 819 and 336 (Euclid’s division algorithm) HCF of 580 and 530 (Euclid’s division algorithm) HCF of 546 and 392 (Euclid’s division algorithm) HCF of 780 and 559 (Euclid’s division algorithm) HCF of 225 and 220 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
30 13 17 21 10 14 13 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 61
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 252. One number is 63. Find the other. HCF of two numbers is 13 and their LCM is 780. One number is 65. Find the other. HCF of two numbers is 7 and their LCM is 280. One number is 35. Find the other. HCF of two numbers is 11 and their LCM is 495. One number is 99. Find the other. HCF of two numbers is 9 and their LCM is 792. One number is 72. Find the other. HCF of two numbers is 5 and their LCM is 90. One number is 10. Find the other.
✅ Answer key — HCF × LCM = product
36 156 56 55 99 45 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 61
Name: Date: Score: / 8
Answer without long division.
Does 1/12 have a terminating decimal expansion? Does 167/176 have a terminating decimal expansion? Does 57/25 have a terminating decimal expansion? Does 41/16 have a terminating decimal expansion? Does 97/125 have a terminating decimal expansion? Does 187/112 have a terminating decimal expansion? Does 149/275 have a terminating decimal expansion? Does 1/6 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5²) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 61
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√14 Rational or irrational: 4 + √21 Rational or irrational: 4√90 Rational or irrational: 1 + √95 Rational or irrational: √59 Rational or irrational: 5 + √9 Rational or irrational: 6 + √67 Rational or irrational: √64 Rational or irrational: 7 + √72 Rational or irrational: √70 Rational or irrational: 9√31 Rational or irrational: √56
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational rational irrational rational 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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