Free · Class 10 · 6 worksheets · answer keys · practise online · set 52
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 52
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2286 Prime factorisation of 1796 Prime factorisation of 1074 Prime factorisation of 2925 Prime factorisation of 2754 Prime factorisation of 2367 Prime factorisation of 1084 Prime factorisation of 1744 Prime factorisation of 830 Prime factorisation of 2793
✅ Answer key — Prime factorisation
2 × 3² × 127 2² × 449 2 × 3 × 179 3² × 5² × 13 2 × 3⁴ × 17 3² × 263 2² × 271 2⁴ × 109 2 × 5 × 83 3 × 7² × 19 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 52
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 10 and 28 HCF and LCM of 133 and 285 HCF and LCM of 24 and 32 HCF and LCM of 18 and 33 HCF and LCM of 39 and 65 HCF and LCM of 60 and 156 HCF and LCM of 16 and 88 HCF and LCM of 112 and 126
✅ Answer key — HCF and LCM
HCF = 2, LCM = 140 HCF = 19, LCM = 1995 HCF = 8, LCM = 96 HCF = 3, LCM = 198 HCF = 13, LCM = 195 HCF = 12, LCM = 780 HCF = 8, LCM = 176 HCF = 14, LCM = 1008 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 52
Name: Date: Score: / 8
Find the HCF.
HCF of 252 and 231 (Euclid’s division algorithm) HCF of 352 and 198 (Euclid’s division algorithm) HCF of 615 and 195 (Euclid’s division algorithm) HCF of 300 and 108 (Euclid’s division algorithm) HCF of 435 and 345 (Euclid’s division algorithm) HCF of 700 and 182 (Euclid’s division algorithm) HCF of 294 and 120 (Euclid’s division algorithm) HCF of 315 and 273 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
21 22 15 12 15 14 6 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 52
Name: Date: Score: / 6
Solve.
HCF of two numbers is 4 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 9 and their LCM is 54. One number is 18. Find the other. HCF of two numbers is 6 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 12 and their LCM is 660. One number is 132. Find the other. HCF of two numbers is 7 and their LCM is 490. One number is 70. Find the other. HCF of two numbers is 10 and their LCM is 330. One number is 110. Find the other.
✅ Answer key — HCF × LCM = product
20 27 30 60 49 30 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 52
Name: Date: Score: / 8
Answer without long division.
Does 71/40 have a terminating decimal expansion? Does 48/25 have a terminating decimal expansion? Does 517/175 have a terminating decimal expansion? Does 9/5 have a terminating decimal expansion? Does 3/56 have a terminating decimal expansion? Does 27/25 have a terminating decimal expansion? Does 41/50 have a terminating decimal expansion? Does 4457/1750 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5²) Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 7) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 52
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 4 + √39 Rational or irrational: 8√32 Rational or irrational: √100 Rational or irrational: √68 Rational or irrational: √81 Rational or irrational: 4√15 Rational or irrational: √14 Rational or irrational: √26 Rational or irrational: 2√64 Rational or irrational: √50 Rational or irrational: 7√67 Rational or irrational: 9 + √59
✅ Answer key — Rational or irrational?
irrational irrational rational irrational rational 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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