Free · Class 10 · 6 worksheets · answer keys · practise online · set 3
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 3
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1334 Prime factorisation of 1659 Prime factorisation of 2672 Prime factorisation of 1479 Prime factorisation of 1884 Prime factorisation of 1702 Prime factorisation of 2500 Prime factorisation of 198 Prime factorisation of 1106 Prime factorisation of 768
✅ Answer key — Prime factorisation
2 × 23 × 29 3 × 7 × 79 2⁴ × 167 3 × 17 × 29 2² × 3 × 157 2 × 23 × 37 2² × 5⁴ 2 × 3² × 11 2 × 7 × 79 2⁸ × 3 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 3
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 60 and 110 HCF and LCM of 182 and 210 HCF and LCM of 112 and 210 HCF and LCM of 34 and 85 HCF and LCM of 88 and 165 HCF and LCM of 81 and 126 HCF and LCM of 8 and 10 HCF and LCM of 15 and 65
✅ Answer key — HCF and LCM
HCF = 10, LCM = 660 HCF = 14, LCM = 2730 HCF = 14, LCM = 1680 HCF = 17, LCM = 170 HCF = 11, LCM = 1320 HCF = 9, LCM = 1134 HCF = 2, LCM = 40 HCF = 5, LCM = 195 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 3
Name: Date: Score: / 8
Find the HCF.
HCF of 676 and 351 (Euclid’s division algorithm) HCF of 936 and 598 (Euclid’s division algorithm) HCF of 220 and 108 (Euclid’s division algorithm) HCF of 544 and 170 (Euclid’s division algorithm) HCF of 531 and 189 (Euclid’s division algorithm) HCF of 424 and 184 (Euclid’s division algorithm) HCF of 760 and 540 (Euclid’s division algorithm) HCF of 441 and 357 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 26 4 34 9 8 20 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 3
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 297. One number is 33. Find the other. HCF of two numbers is 15 and their LCM is 525. One number is 105. Find the other. HCF of two numbers is 7 and their LCM is 539. One number is 49. Find the other. HCF of two numbers is 8 and their LCM is 264. One number is 24. Find the other. HCF of two numbers is 5 and their LCM is 150. One number is 50. Find the other. HCF of two numbers is 8 and their LCM is 144. One number is 16. Find the other.
✅ Answer key — HCF × LCM = product
27 75 77 88 15 72 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 3
Name: Date: Score: / 8
Answer without long division.
Does 57/20 have a terminating decimal expansion? Does 19/22 have a terminating decimal expansion? Does 167/100 have a terminating decimal expansion? Does 3/2 have a terminating decimal expansion? Does 5033/2000 have a terminating decimal expansion? Does 1623/1250 have a terminating decimal expansion? Does 55/28 have a terminating decimal expansion? Does 38/25 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2² × 5) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 2) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 7) 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 3
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 4 + √59 Rational or irrational: 5 + √25 Rational or irrational: 5√51 Rational or irrational: √61 Rational or irrational: 3 + √36 Rational or irrational: 7 + √67 Rational or irrational: 8 + √94 Rational or irrational: 7 + √65 Rational or irrational: 3√20 Rational or irrational: 5√89 Rational or irrational: 2 + √78 Rational or irrational: √43
✅ Answer key — Rational or irrational?
irrational rational irrational 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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