Free · Class 10 · 6 worksheets · answer keys · practise online · set 42
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 42
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1532 Prime factorisation of 494 Prime factorisation of 2626 Prime factorisation of 1204 Prime factorisation of 2943 Prime factorisation of 2706 Prime factorisation of 138 Prime factorisation of 171 Prime factorisation of 1518 Prime factorisation of 1252
✅ Answer key — Prime factorisation
2² × 383 2 × 13 × 19 2 × 13 × 101 2² × 7 × 43 3³ × 109 2 × 3 × 11 × 41 2 × 3 × 23 3² × 19 2 × 3 × 11 × 23 2² × 313 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 42
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 104 and 117 HCF and LCM of 228 and 247 HCF and LCM of 108 and 117 HCF and LCM of 120 and 260 HCF and LCM of 121 and 154 HCF and LCM of 36 and 44 HCF and LCM of 36 and 234 HCF and LCM of 36 and 54
✅ Answer key — HCF and LCM
HCF = 13, LCM = 936 HCF = 19, LCM = 2964 HCF = 9, LCM = 1404 HCF = 20, LCM = 1560 HCF = 11, LCM = 1694 HCF = 4, LCM = 396 HCF = 18, LCM = 468 HCF = 18, LCM = 108 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 42
Name: Date: Score: / 8
Find the HCF.
HCF of 400 and 352 (Euclid’s division algorithm) HCF of 205 and 180 (Euclid’s division algorithm) HCF of 351 and 247 (Euclid’s division algorithm) HCF of 700 and 658 (Euclid’s division algorithm) HCF of 767 and 429 (Euclid’s division algorithm) HCF of 961 and 744 (Euclid’s division algorithm) HCF of 531 and 306 (Euclid’s division algorithm) HCF of 261 and 189 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
16 5 13 14 13 31 9 9 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 42
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 630. One number is 90. Find the other. HCF of two numbers is 5 and their LCM is 50. One number is 25. 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 10 and their LCM is 240. One number is 30. Find the other. HCF of two numbers is 3 and their LCM is 297. One number is 33. Find the other. HCF of two numbers is 8 and their LCM is 320. One number is 64. Find the other.
✅ Answer key — HCF × LCM = product
70 10 48 80 27 40 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 42
Name: Date: Score: / 8
Answer without long division.
Does 854/625 have a terminating decimal expansion? Does 1381/500 have a terminating decimal expansion? Does 109/100 have a terminating decimal expansion? Does 4/5 have a terminating decimal expansion? Does 15/8 have a terminating decimal expansion? Does 52/125 have a terminating decimal expansion? Does 79/28 have a terminating decimal expansion? Does 533/550 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 5) Yes — terminating (denominator 2³) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 7) 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 42
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√49 Rational or irrational: 3√100 Rational or irrational: 1 + √49 Rational or irrational: √77 Rational or irrational: 7 + √6 Rational or irrational: 3√85 Rational or irrational: 3√70 Rational or irrational: √55 Rational or irrational: 7 + √9 Rational or irrational: 1√24 Rational or irrational: √89 Rational or irrational: 8√35
✅ Answer key — Rational or irrational?
rational rational rational irrational irrational irrational irrational irrational rational 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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