Free · Class 10 · 6 worksheets · answer keys · practise online · set 39
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 39
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2568 Prime factorisation of 2016 Prime factorisation of 264 Prime factorisation of 2464 Prime factorisation of 348 Prime factorisation of 608 Prime factorisation of 1702 Prime factorisation of 2262 Prime factorisation of 1770 Prime factorisation of 2226
✅ Answer key — Prime factorisation
2³ × 3 × 107 2⁵ × 3² × 7 2³ × 3 × 11 2⁵ × 7 × 11 2² × 3 × 29 2⁵ × 19 2 × 23 × 37 2 × 3 × 13 × 29 2 × 3 × 5 × 59 2 × 3 × 7 × 53 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 39
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 8 and 26 HCF and LCM of 132 and 180 HCF and LCM of 98 and 182 HCF and LCM of 80 and 90 HCF and LCM of 10 and 55 HCF and LCM of 64 and 104 HCF and LCM of 34 and 187 HCF and LCM of 154 and 196
✅ Answer key — HCF and LCM
HCF = 2, LCM = 104 HCF = 12, LCM = 1980 HCF = 14, LCM = 1274 HCF = 10, LCM = 720 HCF = 5, LCM = 110 HCF = 8, LCM = 832 HCF = 17, LCM = 374 HCF = 14, LCM = 2156 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 39
Name: Date: Score: / 8
Find the HCF.
HCF of 888 and 360 (Euclid’s division algorithm) HCF of 168 and 100 (Euclid’s division algorithm) HCF of 689 and 637 (Euclid’s division algorithm) HCF of 660 and 380 (Euclid’s division algorithm) HCF of 814 and 703 (Euclid’s division algorithm) HCF of 205 and 130 (Euclid’s division algorithm) HCF of 168 and 164 (Euclid’s division algorithm) HCF of 154 and 133 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
24 4 13 20 37 5 4 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 39
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 40. One number is 8. Find the other. HCF of two numbers is 2 and their LCM is 60. One number is 20. Find the other. HCF of two numbers is 5 and their LCM is 275. One number is 55. Find the other. HCF of two numbers is 14 and their LCM is 770. One number is 70. 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 220. One number is 20. Find the other.
✅ Answer key — HCF × LCM = product
10 6 25 154 49 110 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 39
Name: Date: Score: / 8
Answer without long division.
Does 59/50 have a terminating decimal expansion? Does 59/22 have a terminating decimal expansion? Does 268/125 have a terminating decimal expansion? Does 49/20 have a terminating decimal expansion? Does 691/400 have a terminating decimal expansion? Does 27/26 have a terminating decimal expansion? Does 17/8 have a terminating decimal expansion? Does 797/1875 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5³) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2³) 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 39
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √88 Rational or irrational: √93 Rational or irrational: 1 + √37 Rational or irrational: 7√95 Rational or irrational: 7√81 Rational or irrational: 6 + √3 Rational or irrational: 3√10 Rational or irrational: √12 Rational or irrational: 8√10 Rational or irrational: 4√32 Rational or irrational: √61 Rational or irrational: 1√74
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational rational 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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