Free · Class 10 · 6 worksheets · answer keys · practise online · set 44
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 44
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 552 Prime factorisation of 1102 Prime factorisation of 231 Prime factorisation of 2835 Prime factorisation of 432 Prime factorisation of 1390 Prime factorisation of 1808 Prime factorisation of 300 Prime factorisation of 714 Prime factorisation of 2988
✅ Answer key — Prime factorisation
2³ × 3 × 23 2 × 19 × 29 3 × 7 × 11 3⁴ × 5 × 7 2⁴ × 3³ 2 × 5 × 139 2⁴ × 113 2² × 3 × 5² 2 × 3 × 7 × 17 2² × 3² × 83 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 44
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 180 and 198 HCF and LCM of 171 and 209 HCF and LCM of 126 and 182 HCF and LCM of 32 and 36 HCF and LCM of 34 and 85 HCF and LCM of 60 and 110 HCF and LCM of 20 and 28 HCF and LCM of 80 and 220
✅ Answer key — HCF and LCM
HCF = 18, LCM = 1980 HCF = 19, LCM = 1881 HCF = 14, LCM = 1638 HCF = 4, LCM = 288 HCF = 17, LCM = 170 HCF = 10, LCM = 660 HCF = 4, LCM = 140 HCF = 20, LCM = 880 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 44
Name: Date: Score: / 8
Find the HCF.
HCF of 726 and 297 (Euclid’s division algorithm) HCF of 918 and 351 (Euclid’s division algorithm) HCF of 530 and 310 (Euclid’s division algorithm) HCF of 375 and 105 (Euclid’s division algorithm) HCF of 560 and 266 (Euclid’s division algorithm) HCF of 434 and 196 (Euclid’s division algorithm) HCF of 714 and 374 (Euclid’s division algorithm) HCF of 240 and 230 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
33 27 10 15 14 14 34 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 44
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 1092. One number is 91. Find the other. HCF of two numbers is 5 and their LCM is 210. One number is 35. Find the other. HCF of two numbers is 7 and their LCM is 70. One number is 14. Find the other. HCF of two numbers is 4 and their LCM is 360. One number is 40. Find the other. HCF of two numbers is 14 and their LCM is 420. One number is 42. Find the other. HCF of two numbers is 12 and their LCM is 432. One number is 48. Find the other.
✅ Answer key — HCF × LCM = product
156 30 35 36 140 108 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 44
Name: Date: Score: / 8
Answer without long division.
Does 683/550 have a terminating decimal expansion? Does 46/25 have a terminating decimal expansion? Does 213/200 have a terminating decimal expansion? Does 293/100 have a terminating decimal expansion? Does 147/400 have a terminating decimal expansion? Does 5/4 have a terminating decimal expansion? Does 733/275 have a terminating decimal expansion? Does 1062/1375 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5²) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 11) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 44
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √89 Rational or irrational: 2√50 Rational or irrational: √74 Rational or irrational: 2√18 Rational or irrational: 9√16 Rational or irrational: √75 Rational or irrational: √57 Rational or irrational: 9√83 Rational or irrational: 5 + √78 Rational or irrational: 3√33 Rational or irrational: 2 + √34 Rational or irrational: 2√27
✅ Answer key — Rational or irrational?
irrational irrational 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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