Free · Class 10 · 6 worksheets · answer keys · practise online
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
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2852 Prime factorisation of 1557 Prime factorisation of 520 Prime factorisation of 1892 Prime factorisation of 2016 Prime factorisation of 875 Prime factorisation of 375 Prime factorisation of 1593 Prime factorisation of 2870 Prime factorisation of 1212
✅ Answer key — Prime factorisation
2² × 23 × 31 3² × 173 2³ × 5 × 13 2² × 11 × 43 2⁵ × 3² × 7 5³ × 7 3 × 5³ 3³ × 59 2 × 5 × 7 × 41 2² × 3 × 101 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 84 and 154 HCF and LCM of 143 and 182 HCF and LCM of 15 and 65 HCF and LCM of 42 and 56 HCF and LCM of 32 and 36 HCF and LCM of 39 and 45 HCF and LCM of 18 and 135 HCF and LCM of 32 and 40
✅ Answer key — HCF and LCM
HCF = 14, LCM = 924 HCF = 13, LCM = 2002 HCF = 5, LCM = 195 HCF = 14, LCM = 168 HCF = 4, LCM = 288 HCF = 3, LCM = 585 HCF = 9, LCM = 270 HCF = 8, LCM = 160 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3
Name: Date: Score: / 8
Find the HCF.
HCF of 658 and 546 (Euclid’s division algorithm) HCF of 918 and 198 (Euclid’s division algorithm) HCF of 627 and 594 (Euclid’s division algorithm) HCF of 897 and 460 (Euclid’s division algorithm) HCF of 288 and 168 (Euclid’s division algorithm) HCF of 602 and 364 (Euclid’s division algorithm) HCF of 240 and 208 (Euclid’s division algorithm) HCF of 690 and 465 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
14 18 33 23 24 14 16 15 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 198. One number is 18. Find the other. HCF of two numbers is 8 and their LCM is 336. One number is 48. Find the other. HCF of two numbers is 4 and their LCM is 160. One number is 20. Find the other. HCF of two numbers is 11 and their LCM is 990. One number is 99. Find the other. HCF of two numbers is 6 and their LCM is 420. One number is 60. Find the other. HCF of two numbers is 13 and their LCM is 1287. One number is 143. Find the other.
✅ Answer key — HCF × LCM = product
99 56 32 110 42 117 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5
Name: Date: Score: / 8
Answer without long division.
Does 13/10 have a terminating decimal expansion? Does 2581/1000 have a terminating decimal expansion? Does 29/16 have a terminating decimal expansion? Does 117/200 have a terminating decimal expansion? Does 77/250 have a terminating decimal expansion? Does 73/100 have a terminating decimal expansion? Does 111/110 have a terminating decimal expansion? Does 27/35 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 11) 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
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8 + √11 Rational or irrational: √9 Rational or irrational: 6√61 Rational or irrational: 2√25 Rational or irrational: 4 + √60 Rational or irrational: 8√87 Rational or irrational: 3 + √43 Rational or irrational: √89 Rational or irrational: √14 Rational or irrational: 9 + √45 Rational or irrational: √13 Rational or irrational: √49
✅ Answer key — Rational or irrational?
irrational rational irrational rational irrational irrational irrational irrational irrational irrational irrational rational 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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