Free · Class 10 · 6 worksheets · answer keys · practise online · set 35
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 35
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2156 Prime factorisation of 2009 Prime factorisation of 1677 Prime factorisation of 385 Prime factorisation of 2466 Prime factorisation of 1365 Prime factorisation of 2007 Prime factorisation of 190 Prime factorisation of 120 Prime factorisation of 2136
✅ Answer key — Prime factorisation
2² × 7² × 11 7² × 41 3 × 13 × 43 5 × 7 × 11 2 × 3² × 137 3 × 5 × 7 × 13 3² × 223 2 × 5 × 19 2³ × 3 × 5 2³ × 3 × 89 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 35
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 20 and 22 HCF and LCM of 40 and 112 HCF and LCM of 63 and 98 HCF and LCM of 6 and 15 HCF and LCM of 77 and 98 HCF and LCM of 66 and 143 HCF and LCM of 12 and 40 HCF and LCM of 32 and 120
✅ Answer key — HCF and LCM
HCF = 2, LCM = 220 HCF = 8, LCM = 560 HCF = 7, LCM = 882 HCF = 3, LCM = 30 HCF = 7, LCM = 1078 HCF = 11, LCM = 858 HCF = 4, LCM = 120 HCF = 8, LCM = 480 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 35
Name: Date: Score: / 8
Find the HCF.
HCF of 560 and 510 (Euclid’s division algorithm) HCF of 575 and 150 (Euclid’s division algorithm) HCF of 423 and 144 (Euclid’s division algorithm) HCF of 530 and 220 (Euclid’s division algorithm) HCF of 984 and 600 (Euclid’s division algorithm) HCF of 531 and 441 (Euclid’s division algorithm) HCF of 407 and 187 (Euclid’s division algorithm) HCF of 705 and 630 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
10 25 9 10 24 9 11 15 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 35
Name: Date: Score: / 6
Solve.
HCF of two numbers is 7 and their LCM is 196. One number is 28. Find the other. HCF of two numbers is 13 and their LCM is 780. One number is 65. Find the other. HCF of two numbers is 5 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 13 and their LCM is 390. One number is 130. Find the other. HCF of two numbers is 6 and their LCM is 270. One number is 54. Find the other. HCF of two numbers is 3 and their LCM is 189. One number is 27. Find the other.
✅ Answer key — HCF × LCM = product
49 156 35 39 30 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 35
Name: Date: Score: / 8
Answer without long division.
Does 1091/880 have a terminating decimal expansion? Does 362/625 have a terminating decimal expansion? Does 23/65 have a terminating decimal expansion? Does 1613/1250 have a terminating decimal expansion? Does 19/8 have a terminating decimal expansion? Does 15/14 have a terminating decimal expansion? Does 171/140 have a terminating decimal expansion? Does 181/208 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2³) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 7) 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 35
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 1 + √69 Rational or irrational: 4 + √34 Rational or irrational: √88 Rational or irrational: √6 Rational or irrational: 3√10 Rational or irrational: 9 + √45 Rational or irrational: √71 Rational or irrational: 8 + √27 Rational or irrational: √69 Rational or irrational: √99 Rational or irrational: 3√56 Rational or irrational: 7√30
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational 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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