Free · Class 10 · 6 worksheets · answer keys · practise online · set 51
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 51
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1648 Prime factorisation of 928 Prime factorisation of 1964 Prime factorisation of 2289 Prime factorisation of 324 Prime factorisation of 1292 Prime factorisation of 1125 Prime factorisation of 612 Prime factorisation of 657 Prime factorisation of 1916
✅ Answer key — Prime factorisation
2⁴ × 103 2⁵ × 29 2² × 491 3 × 7 × 109 2² × 3⁴ 2² × 17 × 19 3² × 5³ 2² × 3² × 17 3² × 73 2² × 479 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 51
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 21 and 28 HCF and LCM of 36 and 99 HCF and LCM of 35 and 98 HCF and LCM of 144 and 160 HCF and LCM of 16 and 60 HCF and LCM of 56 and 77 HCF and LCM of 98 and 105 HCF and LCM of 221 and 238
✅ Answer key — HCF and LCM
HCF = 7, LCM = 84 HCF = 9, LCM = 396 HCF = 7, LCM = 490 HCF = 16, LCM = 1440 HCF = 4, LCM = 240 HCF = 7, LCM = 616 HCF = 7, LCM = 1470 HCF = 17, LCM = 3094 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 51
Name: Date: Score: / 8
Find the HCF.
HCF of 264 and 200 (Euclid’s division algorithm) HCF of 714 and 231 (Euclid’s division algorithm) HCF of 132 and 108 (Euclid’s division algorithm) HCF of 440 and 280 (Euclid’s division algorithm) HCF of 608 and 384 (Euclid’s division algorithm) HCF of 352 and 154 (Euclid’s division algorithm) HCF of 980 and 300 (Euclid’s division algorithm) HCF of 490 and 180 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
8 21 12 40 32 22 20 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 51
Name: Date: Score: / 6
Solve.
HCF of two numbers is 4 and their LCM is 280. One number is 28. Find the other. HCF of two numbers is 6 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 12 and their LCM is 180. One number is 36. Find the other. HCF of two numbers is 8 and their LCM is 280. One number is 56. Find the other. HCF of two numbers is 11 and their LCM is 165. One number is 33. Find the other. HCF of two numbers is 5 and their LCM is 165. One number is 55. Find the other.
✅ Answer key — HCF × LCM = product
40 30 60 40 55 15 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 51
Name: Date: Score: / 8
Answer without long division.
Does 5/2 have a terminating decimal expansion? Does 2089/1250 have a terminating decimal expansion? Does 681/400 have a terminating decimal expansion? Does 358/125 have a terminating decimal expansion? Does 113/44 have a terminating decimal expansion? Does 267/520 have a terminating decimal expansion? Does 1408/625 have a terminating decimal expansion? Does 7/8 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 51
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9√100 Rational or irrational: √56 Rational or irrational: 2√71 Rational or irrational: 8√91 Rational or irrational: 7 + √3 Rational or irrational: 1 + √46 Rational or irrational: 5 + √71 Rational or irrational: √7 Rational or irrational: √47 Rational or irrational: 3√66 Rational or irrational: √67 Rational or irrational: √43
✅ Answer key — Rational or irrational?
rational 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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