Free · Class 10 · 6 worksheets · answer keys · practise online · set 58
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 58
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2009 Prime factorisation of 735 Prime factorisation of 2511 Prime factorisation of 1710 Prime factorisation of 2988 Prime factorisation of 2130 Prime factorisation of 2752 Prime factorisation of 1830 Prime factorisation of 1695 Prime factorisation of 1530
✅ Answer key — Prime factorisation
7² × 41 3 × 5 × 7² 3⁴ × 31 2 × 3² × 5 × 19 2² × 3² × 83 2 × 3 × 5 × 71 2⁶ × 43 2 × 3 × 5 × 61 3 × 5 × 113 2 × 3² × 5 × 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 58
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 90 and 108 HCF and LCM of 102 and 119 HCF and LCM of 140 and 200 HCF and LCM of 52 and 60 HCF and LCM of 35 and 42 HCF and LCM of 50 and 140 HCF and LCM of 33 and 39 HCF and LCM of 51 and 68
✅ Answer key — HCF and LCM
HCF = 18, LCM = 540 HCF = 17, LCM = 714 HCF = 20, LCM = 1400 HCF = 4, LCM = 780 HCF = 7, LCM = 210 HCF = 10, LCM = 700 HCF = 3, LCM = 429 HCF = 17, LCM = 204 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 58
Name: Date: Score: / 8
Find the HCF.
HCF of 780 and 182 (Euclid’s division algorithm) HCF of 864 and 592 (Euclid’s division algorithm) HCF of 495 and 462 (Euclid’s division algorithm) HCF of 539 and 341 (Euclid’s division algorithm) HCF of 464 and 344 (Euclid’s division algorithm) HCF of 590 and 260 (Euclid’s division algorithm) HCF of 340 and 330 (Euclid’s division algorithm) HCF of 855 and 323 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
26 16 33 11 8 10 10 19 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 58
Name: Date: Score: / 6
Solve.
HCF of two numbers is 7 and their LCM is 588. One number is 84. Find the other. HCF of two numbers is 8 and their LCM is 448. One number is 56. Find the other. HCF of two numbers is 6 and their LCM is 660. One number is 60. Find the other. HCF of two numbers is 7 and their LCM is 168. One number is 21. Find the other. HCF of two numbers is 15 and their LCM is 1320. One number is 165. Find the other. HCF of two numbers is 6 and their LCM is 198. One number is 18. Find the other.
✅ Answer key — HCF × LCM = product
49 64 66 56 120 66 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 58
Name: Date: Score: / 8
Answer without long division.
Does 197/200 have a terminating decimal expansion? Does 253/300 have a terminating decimal expansion? Does 13/15 have a terminating decimal expansion? Does 1731/1250 have a terminating decimal expansion? Does 477/175 have a terminating decimal expansion? Does 3/5 have a terminating decimal expansion? Does 23/25 have a terminating decimal expansion? Does 9/4 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³ × 5²) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5) Yes — terminating (denominator 5²) Yes — terminating (denominator 2²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 58
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 7 + √54 Rational or irrational: 6√19 Rational or irrational: √54 Rational or irrational: 6√35 Rational or irrational: 4√93 Rational or irrational: 9 + √5 Rational or irrational: 5 + √62 Rational or irrational: 8 + √55 Rational or irrational: 3 + √99 Rational or irrational: 3 + √46 Rational or irrational: 3 + √24 Rational or irrational: 6√2
✅ 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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