Free · Class 10 · 6 worksheets · answer keys · practise online · set 87
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 87
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 548 Prime factorisation of 340 Prime factorisation of 2576 Prime factorisation of 2934 Prime factorisation of 2370 Prime factorisation of 1629 Prime factorisation of 987 Prime factorisation of 2829 Prime factorisation of 1519 Prime factorisation of 1868
✅ Answer key — Prime factorisation
2² × 137 2² × 5 × 17 2⁴ × 7 × 23 2 × 3² × 163 2 × 3 × 5 × 79 3² × 181 3 × 7 × 47 3 × 23 × 41 7² × 31 2² × 467 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 87
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 57 and 95 HCF and LCM of 20 and 65 HCF and LCM of 35 and 77 HCF and LCM of 39 and 42 HCF and LCM of 64 and 144 HCF and LCM of 99 and 135 HCF and LCM of 50 and 90 HCF and LCM of 132 and 156
✅ Answer key — HCF and LCM
HCF = 19, LCM = 285 HCF = 5, LCM = 260 HCF = 7, LCM = 385 HCF = 3, LCM = 546 HCF = 16, LCM = 576 HCF = 9, LCM = 1485 HCF = 10, LCM = 450 HCF = 12, LCM = 1716 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 87
Name: Date: Score: / 8
Find the HCF.
HCF of 546 and 338 (Euclid’s division algorithm) HCF of 660 and 285 (Euclid’s division algorithm) HCF of 624 and 117 (Euclid’s division algorithm) HCF of 700 and 406 (Euclid’s division algorithm) HCF of 280 and 192 (Euclid’s division algorithm) HCF of 527 and 153 (Euclid’s division algorithm) HCF of 320 and 248 (Euclid’s division algorithm) HCF of 544 and 128 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
26 15 39 14 8 17 8 32 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 87
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 10 and their LCM is 200. One number is 50. Find the other. HCF of two numbers is 6 and their LCM is 60. One number is 30. Find the other. HCF of two numbers is 13 and their LCM is 312. One number is 39. Find the other. HCF of two numbers is 8 and their LCM is 880. One number is 80. Find the other. HCF of two numbers is 7 and their LCM is 168. One number is 21. Find the other.
✅ Answer key — HCF × LCM = product
15 40 12 104 88 56 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 87
Name: Date: Score: / 8
Answer without long division.
Does 255/112 have a terminating decimal expansion? Does 1391/500 have a terminating decimal expansion? Does 39/20 have a terminating decimal expansion? Does 163/125 have a terminating decimal expansion? Does 409/250 have a terminating decimal expansion? Does 45/16 have a terminating decimal expansion? Does 11/4 have a terminating decimal expansion? Does 1023/500 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 5³) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 2²) Yes — terminating (denominator 2² × 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 87
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√85 Rational or irrational: 4√93 Rational or irrational: 2 + √77 Rational or irrational: √36 Rational or irrational: 1 + √97 Rational or irrational: 8√60 Rational or irrational: √23 Rational or irrational: 3 + √67 Rational or irrational: √91 Rational or irrational: 6 + √54 Rational or irrational: √31 Rational or irrational: √6
✅ Answer key — Rational or irrational?
irrational irrational irrational rational 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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