Free · Class 10 · 6 worksheets · answer keys · practise online · set 46
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 46
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 796 Prime factorisation of 2640 Prime factorisation of 555 Prime factorisation of 418 Prime factorisation of 2905 Prime factorisation of 1312 Prime factorisation of 2375 Prime factorisation of 1088 Prime factorisation of 2070 Prime factorisation of 1998
✅ Answer key — Prime factorisation
2² × 199 2⁴ × 3 × 5 × 11 3 × 5 × 37 2 × 11 × 19 5 × 7 × 83 2⁵ × 41 5³ × 19 2⁶ × 17 2 × 3² × 5 × 23 2 × 3³ × 37 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 46
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 15 and 39 HCF and LCM of 30 and 66 HCF and LCM of 132 and 168 HCF and LCM of 120 and 130 HCF and LCM of 60 and 70 HCF and LCM of 165 and 225 HCF and LCM of 33 and 44 HCF and LCM of 56 and 70
✅ Answer key — HCF and LCM
HCF = 3, LCM = 195 HCF = 6, LCM = 330 HCF = 12, LCM = 1848 HCF = 10, LCM = 1560 HCF = 10, LCM = 420 HCF = 15, LCM = 2475 HCF = 11, LCM = 132 HCF = 14, LCM = 280 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 46
Name: Date: Score: / 8
Find the HCF.
HCF of 767 and 273 (Euclid’s division algorithm) HCF of 477 and 126 (Euclid’s division algorithm) HCF of 256 and 152 (Euclid’s division algorithm) HCF of 910 and 665 (Euclid’s division algorithm) HCF of 470 and 100 (Euclid’s division algorithm) HCF of 286 and 242 (Euclid’s division algorithm) HCF of 735 and 690 (Euclid’s division algorithm) HCF of 697 and 578 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 9 8 35 10 22 15 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 46
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 630. One number is 63. Find the other. HCF of two numbers is 9 and their LCM is 315. One number is 45. Find the other. HCF of two numbers is 10 and their LCM is 150. One number is 30. Find the other. HCF of two numbers is 15 and their LCM is 270. One number is 135. Find the other. HCF of two numbers is 2 and their LCM is 40. One number is 8. Find the other. HCF of two numbers is 8 and their LCM is 320. One number is 40. Find the other.
✅ Answer key — HCF × LCM = product
90 63 50 30 10 64 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 46
Name: Date: Score: / 8
Answer without long division.
Does 279/2000 have a terminating decimal expansion? Does 159/110 have a terminating decimal expansion? Does 57/70 have a terminating decimal expansion? Does 13/16 have a terminating decimal expansion? Does 199/240 have a terminating decimal expansion? Does 63/125 have a terminating decimal expansion? Does 197/80 have a terminating decimal expansion? Does 61/30 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2⁴) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5³) Yes — terminating (denominator 2⁴ × 5) 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 46
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √78 Rational or irrational: 5√69 Rational or irrational: √65 Rational or irrational: 6 + √35 Rational or irrational: 2 + √37 Rational or irrational: 8 + √37 Rational or irrational: 3√8 Rational or irrational: √29 Rational or irrational: 1√79 Rational or irrational: 5√48 Rational or irrational: 1 + √8 Rational or irrational: 5 + √7
✅ 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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