Free · Class 10 · 6 worksheets · answer keys · practise online · set 7
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 7
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 138 Prime factorisation of 465 Prime factorisation of 588 Prime factorisation of 168 Prime factorisation of 660 Prime factorisation of 116 Prime factorisation of 2163 Prime factorisation of 462 Prime factorisation of 2416 Prime factorisation of 772
✅ Answer key — Prime factorisation
2 × 3 × 23 3 × 5 × 31 2² × 3 × 7² 2³ × 3 × 7 2² × 3 × 5 × 11 2² × 29 3 × 7 × 103 2 × 3 × 7 × 11 2⁴ × 151 2² × 193 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 7
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 65 and 182 HCF and LCM of 70 and 77 HCF and LCM of 40 and 64 HCF and LCM of 48 and 160 HCF and LCM of 16 and 72 HCF and LCM of 84 and 156 HCF and LCM of 36 and 52 HCF and LCM of 40 and 260
✅ Answer key — HCF and LCM
HCF = 13, LCM = 910 HCF = 7, LCM = 770 HCF = 8, LCM = 320 HCF = 16, LCM = 480 HCF = 8, LCM = 144 HCF = 12, LCM = 1092 HCF = 4, LCM = 468 HCF = 20, LCM = 520 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 7
Name: Date: Score: / 8
Find the HCF.
HCF of 672 and 360 (Euclid’s division algorithm) HCF of 840 and 322 (Euclid’s division algorithm) HCF of 703 and 646 (Euclid’s division algorithm) HCF of 600 and 495 (Euclid’s division algorithm) HCF of 540 and 477 (Euclid’s division algorithm) HCF of 580 and 250 (Euclid’s division algorithm) HCF of 912 and 133 (Euclid’s division algorithm) HCF of 861 and 189 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
24 14 19 15 9 10 19 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 7
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 132. One number is 44. Find the other. HCF of two numbers is 11 and their LCM is 242. One number is 22. Find the other. HCF of two numbers is 6 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 5 and their LCM is 220. One number is 20. Find the other. HCF of two numbers is 15 and their LCM is 1980. One number is 165. Find the other. HCF of two numbers is 12 and their LCM is 1584. One number is 132. Find the other.
✅ Answer key — HCF × LCM = product
33 121 30 55 180 144 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 7
Name: Date: Score: / 8
Answer without long division.
Does 21/8 have a terminating decimal expansion? Does 9/10 have a terminating decimal expansion? Does 1403/600 have a terminating decimal expansion? Does 33/16 have a terminating decimal expansion? Does 1249/1100 have a terminating decimal expansion? Does 633/220 have a terminating decimal expansion? Does 215/208 have a terminating decimal expansion? Does 451/200 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³) Yes — terminating (denominator 2 × 5) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2⁴) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2³ × 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 7
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 4 + √33 Rational or irrational: √39 Rational or irrational: 6 + √92 Rational or irrational: 5 + √19 Rational or irrational: 7√56 Rational or irrational: √5 Rational or irrational: 9√86 Rational or irrational: √7 Rational or irrational: 6√46 Rational or irrational: 8√96 Rational or irrational: √55 Rational or irrational: 5√94
✅ 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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