Free · Class 10 · 6 worksheets · answer keys · practise online · set 25
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 25
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1200 Prime factorisation of 2348 Prime factorisation of 2904 Prime factorisation of 510 Prime factorisation of 1833 Prime factorisation of 2170 Prime factorisation of 1539 Prime factorisation of 2586 Prime factorisation of 1668 Prime factorisation of 1593
✅ Answer key — Prime factorisation
2⁴ × 3 × 5² 2² × 587 2³ × 3 × 11² 2 × 3 × 5 × 17 3 × 13 × 47 2 × 5 × 7 × 31 3⁴ × 19 2 × 3 × 431 2² × 3 × 139 3³ × 59 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 25
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 14 and 49 HCF and LCM of 90 and 99 HCF and LCM of 112 and 208 HCF and LCM of 112 and 160 HCF and LCM of 36 and 90 HCF and LCM of 252 and 270 HCF and LCM of 40 and 180 HCF and LCM of 40 and 112
✅ Answer key — HCF and LCM
HCF = 7, LCM = 98 HCF = 9, LCM = 990 HCF = 16, LCM = 1456 HCF = 16, LCM = 1120 HCF = 18, LCM = 180 HCF = 18, LCM = 3780 HCF = 20, LCM = 360 HCF = 8, LCM = 560 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 25
Name: Date: Score: / 8
Find the HCF.
HCF of 840 and 520 (Euclid’s division algorithm) HCF of 598 and 391 (Euclid’s division algorithm) HCF of 451 and 286 (Euclid’s division algorithm) HCF of 516 and 468 (Euclid’s division algorithm) HCF of 280 and 270 (Euclid’s division algorithm) HCF of 280 and 240 (Euclid’s division algorithm) HCF of 272 and 168 (Euclid’s division algorithm) HCF of 322 and 133 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
40 23 11 12 10 40 8 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 25
Name: Date: Score: / 6
Solve.
HCF of two numbers is 5 and their LCM is 60. One number is 15. Find the other. HCF of two numbers is 9 and their LCM is 594. One number is 54. Find the other. HCF of two numbers is 13 and their LCM is 364. One number is 52. Find the other. HCF of two numbers is 4 and their LCM is 396. One number is 36. Find the other. HCF of two numbers is 12 and their LCM is 504. One number is 72. Find the other. HCF of two numbers is 4 and their LCM is 120. One number is 20. Find the other.
✅ Answer key — HCF × LCM = product
20 99 91 44 84 24 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 25
Name: Date: Score: / 8
Answer without long division.
Does 52/25 have a terminating decimal expansion? Does 1073/375 have a terminating decimal expansion? Does 59/20 have a terminating decimal expansion? Does 357/1000 have a terminating decimal expansion? Does 93/260 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 1453/520 have a terminating decimal expansion? Does 13/10 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 2³ × 5³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2 × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 25
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 3√24 Rational or irrational: √88 Rational or irrational: 9√100 Rational or irrational: 8 + √78 Rational or irrational: √49 Rational or irrational: 2√48 Rational or irrational: √47 Rational or irrational: 6√65 Rational or irrational: √77 Rational or irrational: √19 Rational or irrational: 7 + √19 Rational or irrational: 2√83
✅ Answer key — Rational or irrational?
irrational irrational rational irrational rational 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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