Free · Class 10 · 6 worksheets · answer keys · practise online · set 8
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 8
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 608 Prime factorisation of 376 Prime factorisation of 408 Prime factorisation of 436 Prime factorisation of 1449 Prime factorisation of 420 Prime factorisation of 640 Prime factorisation of 2774 Prime factorisation of 2639 Prime factorisation of 2715
✅ Answer key — Prime factorisation
2⁵ × 19 2³ × 47 2³ × 3 × 17 2² × 109 3² × 7 × 23 2² × 3 × 5 × 7 2⁷ × 5 2 × 19 × 73 7 × 13 × 29 3 × 5 × 181 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 8
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 126 and 234 HCF and LCM of 168 and 182 HCF and LCM of 80 and 300 HCF and LCM of 65 and 156 HCF and LCM of 18 and 48 HCF and LCM of 143 and 165 HCF and LCM of 33 and 42 HCF and LCM of 195 and 210
✅ Answer key — HCF and LCM
HCF = 18, LCM = 1638 HCF = 14, LCM = 2184 HCF = 20, LCM = 1200 HCF = 13, LCM = 780 HCF = 6, LCM = 144 HCF = 11, LCM = 2145 HCF = 3, LCM = 462 HCF = 15, LCM = 2730 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 8
Name: Date: Score: / 8
Find the HCF.
HCF of 651 and 310 (Euclid’s division algorithm) HCF of 624 and 496 (Euclid’s division algorithm) HCF of 900 and 640 (Euclid’s division algorithm) HCF of 814 and 352 (Euclid’s division algorithm) HCF of 162 and 132 (Euclid’s division algorithm) HCF of 925 and 275 (Euclid’s division algorithm) HCF of 295 and 170 (Euclid’s division algorithm) HCF of 330 and 246 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
31 16 20 22 6 25 5 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 8
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 572. One number is 143. Find the other. HCF of two numbers is 2 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 4 and their LCM is 220. One number is 20. Find the other. HCF of two numbers is 6 and their LCM is 270. One number is 30. Find the other. HCF of two numbers is 6 and their LCM is 336. 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
52 10 44 54 48 108 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 8
Name: Date: Score: / 8
Answer without long division.
Does 803/1040 have a terminating decimal expansion? Does 29/200 have a terminating decimal expansion? Does 348/625 have a terminating decimal expansion? Does 4981/2000 have a terminating decimal expansion? Does 2346/875 have a terminating decimal expansion? Does 2993/1000 have a terminating decimal expansion? Does 1/5 have a terminating decimal expansion? Does 1379/650 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³ × 5³) Yes — terminating (denominator 5) 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 8
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 5 + √59 Rational or irrational: 6√49 Rational or irrational: 6√19 Rational or irrational: 3 + √55 Rational or irrational: √55 Rational or irrational: √41 Rational or irrational: 6√39 Rational or irrational: 6√59 Rational or irrational: 6√86 Rational or irrational: 7√5 Rational or irrational: √6 Rational or irrational: √79
✅ Answer key — Rational or irrational?
irrational rational 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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