Free · Class 10 · 6 worksheets · answer keys · practise online · set 75
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 75
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1342 Prime factorisation of 1482 Prime factorisation of 1498 Prime factorisation of 1755 Prime factorisation of 2836 Prime factorisation of 856 Prime factorisation of 2682 Prime factorisation of 1500 Prime factorisation of 652 Prime factorisation of 1000
✅ Answer key — Prime factorisation
2 × 11 × 61 2 × 3 × 13 × 19 2 × 7 × 107 3³ × 5 × 13 2² × 709 2³ × 107 2 × 3² × 149 2² × 3 × 5³ 2² × 163 2³ × 5³ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 75
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 45 and 108 HCF and LCM of 140 and 154 HCF and LCM of 40 and 90 HCF and LCM of 16 and 88 HCF and LCM of 126 and 162 HCF and LCM of 24 and 84 HCF and LCM of 28 and 63 HCF and LCM of 48 and 66
✅ Answer key — HCF and LCM
HCF = 9, LCM = 540 HCF = 14, LCM = 1540 HCF = 10, LCM = 360 HCF = 8, LCM = 176 HCF = 18, LCM = 1134 HCF = 12, LCM = 168 HCF = 7, LCM = 252 HCF = 6, LCM = 528 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 75
Name: Date: Score: / 8
Find the HCF.
HCF of 598 and 130 (Euclid’s division algorithm) HCF of 318 and 312 (Euclid’s division algorithm) HCF of 800 and 224 (Euclid’s division algorithm) HCF of 645 and 525 (Euclid’s division algorithm) HCF of 516 and 252 (Euclid’s division algorithm) HCF of 459 and 333 (Euclid’s division algorithm) HCF of 207 and 117 (Euclid’s division algorithm) HCF of 663 and 119 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
26 6 32 15 12 9 9 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 75
Name: Date: Score: / 6
Solve.
HCF of two numbers is 14 and their LCM is 280. One number is 56. Find the other. HCF of two numbers is 6 and their LCM is 540. One number is 60. Find the other. HCF of two numbers is 6 and their LCM is 132. One number is 12. Find the other. HCF of two numbers is 6 and their LCM is 528. One number is 48. Find the other. HCF of two numbers is 14 and their LCM is 980. One number is 140. Find the other. HCF of two numbers is 9 and their LCM is 252. One number is 63. Find the other.
✅ Answer key — HCF × LCM = product
70 54 66 66 98 36 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 75
Name: Date: Score: / 8
Answer without long division.
Does 3059/2000 have a terminating decimal expansion? Does 2921/1100 have a terminating decimal expansion? Does 92/75 have a terminating decimal expansion? Does 237/400 have a terminating decimal expansion? Does 4/5 have a terminating decimal expansion? Does 26/35 have a terminating decimal expansion? Does 149/110 have a terminating decimal expansion? Does 7/4 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 3) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 75
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9√26 Rational or irrational: √85 Rational or irrational: 1√100 Rational or irrational: 1 + √49 Rational or irrational: 3√41 Rational or irrational: 6 + √13 Rational or irrational: √14 Rational or irrational: 7√29 Rational or irrational: √69 Rational or irrational: 3√23 Rational or irrational: √62 Rational or irrational: √68
✅ Answer key — Rational or irrational?
irrational irrational rational 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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