Free · Class 10 · 6 worksheets · answer keys · practise online · set 18
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 18
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 833 Prime factorisation of 686 Prime factorisation of 135 Prime factorisation of 1368 Prime factorisation of 1356 Prime factorisation of 740 Prime factorisation of 285 Prime factorisation of 1880 Prime factorisation of 195 Prime factorisation of 1730
✅ Answer key — Prime factorisation
7² × 17 2 × 7³ 3³ × 5 2³ × 3² × 19 2² × 3 × 113 2² × 5 × 37 3 × 5 × 19 2³ × 5 × 47 3 × 5 × 13 2 × 5 × 173 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 18
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 60 and 100 HCF and LCM of 27 and 42 HCF and LCM of 18 and 84 HCF and LCM of 22 and 77 HCF and LCM of 108 and 126 HCF and LCM of 56 and 126 HCF and LCM of 187 and 238 HCF and LCM of 21 and 91
✅ Answer key — HCF and LCM
HCF = 20, LCM = 300 HCF = 3, LCM = 378 HCF = 6, LCM = 252 HCF = 11, LCM = 154 HCF = 18, LCM = 756 HCF = 14, LCM = 504 HCF = 17, LCM = 2618 HCF = 7, LCM = 273 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 18
Name: Date: Score: / 8
Find the HCF.
HCF of 912 and 361 (Euclid’s division algorithm) HCF of 552 and 324 (Euclid’s division algorithm) HCF of 580 and 190 (Euclid’s division algorithm) HCF of 756 and 490 (Euclid’s division algorithm) HCF of 936 and 744 (Euclid’s division algorithm) HCF of 228 and 200 (Euclid’s division algorithm) HCF of 420 and 399 (Euclid’s division algorithm) HCF of 754 and 221 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
19 12 10 14 24 4 21 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 18
Name: Date: Score: / 6
Solve.
HCF of two numbers is 4 and their LCM is 88. One number is 44. Find the other. HCF of two numbers is 9 and their LCM is 90. One number is 18. Find the other. HCF of two numbers is 5 and their LCM is 225. One number is 25. Find the other. HCF of two numbers is 6 and their LCM is 180. One number is 60. Find the other. HCF of two numbers is 5 and their LCM is 110. One number is 10. Find the other. HCF of two numbers is 5 and their LCM is 110. One number is 55. Find the other.
✅ Answer key — HCF × LCM = product
8 45 45 18 55 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 18
Name: Date: Score: / 8
Answer without long division.
Does 457/175 have a terminating decimal expansion? Does 13/8 have a terminating decimal expansion? Does 7/16 have a terminating decimal expansion? Does 629/1100 have a terminating decimal expansion? Does 21/16 have a terminating decimal expansion? Does 55/24 have a terminating decimal expansion? Does 1/30 have a terminating decimal expansion? Does 109/60 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³) Yes — terminating (denominator 2⁴) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 18
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √76 Rational or irrational: 4√99 Rational or irrational: 6 + √54 Rational or irrational: 3 + √88 Rational or irrational: 8 + √85 Rational or irrational: √47 Rational or irrational: 3√67 Rational or irrational: √28 Rational or irrational: 3 + √37 Rational or irrational: 6√75 Rational or irrational: √66 Rational or irrational: √70
✅ 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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