Free · Class 10 · 6 worksheets · answer keys · practise online · set 30
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 30
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2950 Prime factorisation of 2202 Prime factorisation of 1470 Prime factorisation of 250 Prime factorisation of 630 Prime factorisation of 2300 Prime factorisation of 988 Prime factorisation of 351 Prime factorisation of 2784 Prime factorisation of 756
✅ Answer key — Prime factorisation
2 × 5² × 59 2 × 3 × 367 2 × 3 × 5 × 7² 2 × 5³ 2 × 3² × 5 × 7 2² × 5² × 23 2² × 13 × 19 3³ × 13 2⁵ × 3 × 29 2² × 3³ × 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 30
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 38 and 95 HCF and LCM of 77 and 121 HCF and LCM of 56 and 70 HCF and LCM of 66 and 77 HCF and LCM of 14 and 21 HCF and LCM of 108 and 120 HCF and LCM of 54 and 72 HCF and LCM of 132 and 156
✅ Answer key — HCF and LCM
HCF = 19, LCM = 190 HCF = 11, LCM = 847 HCF = 14, LCM = 280 HCF = 11, LCM = 462 HCF = 7, LCM = 42 HCF = 12, LCM = 1080 HCF = 18, LCM = 216 HCF = 12, LCM = 1716 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 30
Name: Date: Score: / 8
Find the HCF.
HCF of 738 and 270 (Euclid’s division algorithm) HCF of 720 and 264 (Euclid’s division algorithm) HCF of 162 and 135 (Euclid’s division algorithm) HCF of 714 and 364 (Euclid’s division algorithm) HCF of 280 and 170 (Euclid’s division algorithm) HCF of 374 and 255 (Euclid’s division algorithm) HCF of 760 and 500 (Euclid’s division algorithm) HCF of 697 and 187 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
18 24 27 14 10 17 20 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 30
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 396. One number is 36. Find the other. HCF of two numbers is 6 and their LCM is 792. One number is 66. Find the other. HCF of two numbers is 7 and their LCM is 210. One number is 35. Find the other. HCF of two numbers is 6 and their LCM is 84. One number is 42. Find the other. HCF of two numbers is 2 and their LCM is 30. One number is 10. Find the other. HCF of two numbers is 3 and their LCM is 165. One number is 15. Find the other.
✅ Answer key — HCF × LCM = product
33 72 42 12 6 33 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 30
Name: Date: Score: / 8
Answer without long division.
Does 1598/875 have a terminating decimal expansion? Does 251/260 have a terminating decimal expansion? Does 113/56 have a terminating decimal expansion? Does 601/500 have a terminating decimal expansion? Does 2991/1375 have a terminating decimal expansion? Does 13/5 have a terminating decimal expansion? Does 3/16 have a terminating decimal expansion? Does 67/25 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 30
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 6 + √11 Rational or irrational: √29 Rational or irrational: √94 Rational or irrational: 1 + √86 Rational or irrational: 4 + √44 Rational or irrational: 3√62 Rational or irrational: 8 + √85 Rational or irrational: 9 + √55 Rational or irrational: √63 Rational or irrational: 9 + √42 Rational or irrational: 8√25 Rational or irrational: √76
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational rational 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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