Free · Class 10 · 6 worksheets · answer keys · practise online · set 60
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 60
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2525 Prime factorisation of 833 Prime factorisation of 1442 Prime factorisation of 414 Prime factorisation of 2370 Prime factorisation of 1331 Prime factorisation of 1989 Prime factorisation of 848 Prime factorisation of 608 Prime factorisation of 942
✅ Answer key — Prime factorisation
5² × 101 7² × 17 2 × 7 × 103 2 × 3² × 23 2 × 3 × 5 × 79 11³ 3² × 13 × 17 2⁴ × 53 2⁵ × 19 2 × 3 × 157 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 60
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 24 and 180 HCF and LCM of 105 and 150 HCF and LCM of 98 and 210 HCF and LCM of 20 and 30 HCF and LCM of 60 and 100 HCF and LCM of 49 and 77 HCF and LCM of 48 and 60 HCF and LCM of 85 and 187
✅ Answer key — HCF and LCM
HCF = 12, LCM = 360 HCF = 15, LCM = 1050 HCF = 14, LCM = 1470 HCF = 10, LCM = 60 HCF = 20, LCM = 300 HCF = 7, LCM = 539 HCF = 12, LCM = 240 HCF = 17, LCM = 935 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 60
Name: Date: Score: / 8
Find the HCF.
HCF of 742 and 252 (Euclid’s division algorithm) HCF of 159 and 126 (Euclid’s division algorithm) HCF of 342 and 198 (Euclid’s division algorithm) HCF of 648 and 120 (Euclid’s division algorithm) HCF of 400 and 288 (Euclid’s division algorithm) HCF of 855 and 836 (Euclid’s division algorithm) HCF of 624 and 252 (Euclid’s division algorithm) HCF of 780 and 210 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
14 3 18 24 16 19 12 30 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 60
Name: Date: Score: / 6
Solve.
HCF of two numbers is 5 and their LCM is 200. One number is 25. Find the other. HCF of two numbers is 7 and their LCM is 616. One number is 77. Find the other. HCF of two numbers is 15 and their LCM is 990. One number is 90. Find the other. HCF of two numbers is 7 and their LCM is 252. One number is 28. Find the other. HCF of two numbers is 14 and their LCM is 882. One number is 126. Find the other. HCF of two numbers is 15 and their LCM is 300. One number is 75. Find the other.
✅ Answer key — HCF × LCM = product
40 56 165 63 98 60 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 60
Name: Date: Score: / 8
Answer without long division.
Does 394/175 have a terminating decimal expansion? Does 63/40 have a terminating decimal expansion? Does 203/125 have a terminating decimal expansion? Does 287/100 have a terminating decimal expansion? Does 474/625 have a terminating decimal expansion? Does 569/250 have a terminating decimal expansion? Does 51/1750 have a terminating decimal expansion? Does 7/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 5³) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2 × 5³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 60
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 7√36 Rational or irrational: √28 Rational or irrational: 2 + √82 Rational or irrational: 2 + √24 Rational or irrational: √32 Rational or irrational: 1√19 Rational or irrational: √89 Rational or irrational: 4√52 Rational or irrational: 4√32 Rational or irrational: √49 Rational or irrational: 5 + √25 Rational or irrational: √65
✅ Answer key — Rational or irrational?
rational irrational irrational irrational irrational irrational irrational irrational irrational rational 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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