Free · Class 10 · 6 worksheets · answer keys · practise online · set 41
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 41
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1892 Prime factorisation of 1017 Prime factorisation of 2162 Prime factorisation of 2555 Prime factorisation of 2706 Prime factorisation of 2523 Prime factorisation of 1715 Prime factorisation of 628 Prime factorisation of 1425 Prime factorisation of 2343
✅ Answer key — Prime factorisation
2² × 11 × 43 3² × 113 2 × 23 × 47 5 × 7 × 73 2 × 3 × 11 × 41 3 × 29² 5 × 7³ 2² × 157 3 × 5² × 19 3 × 11 × 71 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 41
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 80 and 192 HCF and LCM of 153 and 221 HCF and LCM of 36 and 198 HCF and LCM of 40 and 110 HCF and LCM of 8 and 30 HCF and LCM of 55 and 99 HCF and LCM of 240 and 260 HCF and LCM of 26 and 117
✅ Answer key — HCF and LCM
HCF = 16, LCM = 960 HCF = 17, LCM = 1989 HCF = 18, LCM = 396 HCF = 10, LCM = 440 HCF = 2, LCM = 120 HCF = 11, LCM = 495 HCF = 20, LCM = 3120 HCF = 13, LCM = 234 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 41
Name: Date: Score: / 8
Find the HCF.
HCF of 391 and 204 (Euclid’s division algorithm) HCF of 752 and 576 (Euclid’s division algorithm) HCF of 672 and 350 (Euclid’s division algorithm) HCF of 950 and 228 (Euclid’s division algorithm) HCF of 234 and 186 (Euclid’s division algorithm) HCF of 910 and 245 (Euclid’s division algorithm) HCF of 767 and 234 (Euclid’s division algorithm) HCF of 837 and 648 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
17 16 14 38 6 35 13 27 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 41
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 28. One number is 4. Find the other. HCF of two numbers is 15 and their LCM is 450. One number is 90. Find the other. HCF of two numbers is 6 and their LCM is 36. One number is 12. Find the other. HCF of two numbers is 10 and their LCM is 770. One number is 110. Find the other. HCF of two numbers is 5 and their LCM is 210. One number is 35. Find the other. HCF of two numbers is 6 and their LCM is 660. One number is 66. Find the other.
✅ Answer key — HCF × LCM = product
14 75 18 70 30 60 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 41
Name: Date: Score: / 8
Answer without long division.
Does 169/280 have a terminating decimal expansion? Does 413/240 have a terminating decimal expansion? Does 1566/1375 have a terminating decimal expansion? Does 183/275 have a terminating decimal expansion? Does 68/125 have a terminating decimal expansion? Does 53/28 have a terminating decimal expansion? Does 814/625 have a terminating decimal expansion? Does 1359/1300 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 13) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 41
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √2 Rational or irrational: 1√67 Rational or irrational: 3√97 Rational or irrational: 8 + √61 Rational or irrational: 7 + √18 Rational or irrational: 6√60 Rational or irrational: 3 + √67 Rational or irrational: 7√23 Rational or irrational: 6 + √40 Rational or irrational: √75 Rational or irrational: √100 Rational or irrational: √68
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational rational 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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