Free · Class 10 · 6 worksheets · answer keys · practise online · set 83
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 83
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2570 Prime factorisation of 2915 Prime factorisation of 1524 Prime factorisation of 2070 Prime factorisation of 360 Prime factorisation of 2635 Prime factorisation of 1228 Prime factorisation of 801 Prime factorisation of 2714 Prime factorisation of 1460
✅ Answer key — Prime factorisation
2 × 5 × 257 5 × 11 × 53 2² × 3 × 127 2 × 3² × 5 × 23 2³ × 3² × 5 5 × 17 × 31 2² × 307 3² × 89 2 × 23 × 59 2² × 5 × 73 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 83
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 50 and 65 HCF and LCM of 80 and 176 HCF and LCM of 128 and 240 HCF and LCM of 112 and 210 HCF and LCM of 18 and 26 HCF and LCM of 30 and 80 HCF and LCM of 18 and 66 HCF and LCM of 54 and 78
✅ Answer key — HCF and LCM
HCF = 5, LCM = 650 HCF = 16, LCM = 880 HCF = 16, LCM = 1920 HCF = 14, LCM = 1680 HCF = 2, LCM = 234 HCF = 10, LCM = 240 HCF = 6, LCM = 198 HCF = 6, LCM = 702 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 83
Name: Date: Score: / 8
Find the HCF.
HCF of 252 and 196 (Euclid’s division algorithm) HCF of 320 and 168 (Euclid’s division algorithm) HCF of 846 and 594 (Euclid’s division algorithm) HCF of 459 and 289 (Euclid’s division algorithm) HCF of 783 and 493 (Euclid’s division algorithm) HCF of 336 and 308 (Euclid’s division algorithm) HCF of 600 and 285 (Euclid’s division algorithm) HCF of 448 and 266 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
28 8 18 17 29 28 15 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 83
Name: Date: Score: / 6
Solve.
HCF of two numbers is 12 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 12 and their LCM is 1320. One number is 132. Find the other. HCF of two numbers is 11 and their LCM is 770. One number is 77. Find the other. HCF of two numbers is 14 and their LCM is 840. One number is 168. Find the other. HCF of two numbers is 5 and their LCM is 385. One number is 55. Find the other. HCF of two numbers is 5 and their LCM is 210. One number is 35. Find the other.
✅ Answer key — HCF × LCM = product
60 120 110 70 35 30 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 83
Name: Date: Score: / 8
Answer without long division.
Does 333/400 have a terminating decimal expansion? Does 203/75 have a terminating decimal expansion? Does 4653/2000 have a terminating decimal expansion? Does 63/40 have a terminating decimal expansion? Does 498/325 have a terminating decimal expansion? Does 449/250 have a terminating decimal expansion? Does 4819/2000 have a terminating decimal expansion? Does 2047/1625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 13) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 83
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 6 + √11 Rational or irrational: 2√82 Rational or irrational: √58 Rational or irrational: 5 + √9 Rational or irrational: 4 + √24 Rational or irrational: √69 Rational or irrational: 3 + √45 Rational or irrational: √33 Rational or irrational: 4√52 Rational or irrational: 4 + √88 Rational or irrational: 4√69 Rational or irrational: 6 + √58
✅ Answer key — Rational or irrational?
irrational irrational irrational rational 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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