Free · Class 10 · 6 worksheets · answer keys · practise online · set 28
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 28
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 652 Prime factorisation of 441 Prime factorisation of 710 Prime factorisation of 750 Prime factorisation of 2670 Prime factorisation of 1786 Prime factorisation of 363 Prime factorisation of 2480 Prime factorisation of 1785 Prime factorisation of 230
✅ Answer key — Prime factorisation
2² × 163 3² × 7² 2 × 5 × 71 2 × 3 × 5³ 2 × 3 × 5 × 89 2 × 19 × 47 3 × 11² 2⁴ × 5 × 31 3 × 5 × 7 × 17 2 × 5 × 23 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 28
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 27 and 117 HCF and LCM of 128 and 144 HCF and LCM of 60 and 100 HCF and LCM of 57 and 133 HCF and LCM of 30 and 33 HCF and LCM of 84 and 90 HCF and LCM of 72 and 78 HCF and LCM of 66 and 72
✅ Answer key — HCF and LCM
HCF = 9, LCM = 351 HCF = 16, LCM = 1152 HCF = 20, LCM = 300 HCF = 19, LCM = 399 HCF = 3, LCM = 330 HCF = 6, LCM = 1260 HCF = 6, LCM = 936 HCF = 6, LCM = 792 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 28
Name: Date: Score: / 8
Find the HCF.
HCF of 368 and 161 (Euclid’s division algorithm) HCF of 627 and 304 (Euclid’s division algorithm) HCF of 530 and 490 (Euclid’s division algorithm) HCF of 555 and 225 (Euclid’s division algorithm) HCF of 940 and 420 (Euclid’s division algorithm) HCF of 432 and 248 (Euclid’s division algorithm) HCF of 290 and 285 (Euclid’s division algorithm) HCF of 295 and 185 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
23 19 10 15 20 8 5 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 28
Name: Date: Score: / 6
Solve.
HCF of two numbers is 5 and their LCM is 30. One number is 10. Find the other. HCF of two numbers is 15 and their LCM is 270. One number is 135. Find the other. HCF of two numbers is 4 and their LCM is 24. One number is 8. Find the other. HCF of two numbers is 15 and their LCM is 1650. One number is 150. Find the other. HCF of two numbers is 12 and their LCM is 216. One number is 24. Find the other. HCF of two numbers is 7 and their LCM is 588. One number is 49. Find the other.
✅ Answer key — HCF × LCM = product
15 30 12 165 108 84 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 28
Name: Date: Score: / 8
Answer without long division.
Does 3/5 have a terminating decimal expansion? Does 59/40 have a terminating decimal expansion? Does 1/8 have a terminating decimal expansion? Does 677/350 have a terminating decimal expansion? Does 52/25 have a terminating decimal expansion? Does 7/8 have a terminating decimal expansion? Does 951/520 have a terminating decimal expansion? Does 23/20 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5) Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 2³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5²) Yes — terminating (denominator 2³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2² × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 28
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 7 + √92 Rational or irrational: 3 + √71 Rational or irrational: 6 + √47 Rational or irrational: 7√10 Rational or irrational: 5 + √74 Rational or irrational: 9√24 Rational or irrational: √23 Rational or irrational: 3 + √11 Rational or irrational: 4√37 Rational or irrational: 6√61 Rational or irrational: 7 + √38 Rational or irrational: 4√77
✅ 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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