Free · Class 10 · 6 worksheets · answer keys · practise online · set 63
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 63
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 896 Prime factorisation of 2450 Prime factorisation of 1815 Prime factorisation of 1846 Prime factorisation of 2163 Prime factorisation of 1110 Prime factorisation of 828 Prime factorisation of 1510 Prime factorisation of 2877 Prime factorisation of 1898
✅ Answer key — Prime factorisation
2⁷ × 7 2 × 5² × 7² 3 × 5 × 11² 2 × 13 × 71 3 × 7 × 103 2 × 3 × 5 × 37 2² × 3² × 23 2 × 5 × 151 3 × 7 × 137 2 × 13 × 73 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 63
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 30 and 55 HCF and LCM of 128 and 208 HCF and LCM of 80 and 110 HCF and LCM of 40 and 104 HCF and LCM of 80 and 260 HCF and LCM of 18 and 135 HCF and LCM of 110 and 120 HCF and LCM of 60 and 96
✅ Answer key — HCF and LCM
HCF = 5, LCM = 330 HCF = 16, LCM = 1664 HCF = 10, LCM = 880 HCF = 8, LCM = 520 HCF = 20, LCM = 1040 HCF = 9, LCM = 270 HCF = 10, LCM = 1320 HCF = 12, LCM = 480 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 63
Name: Date: Score: / 8
Find the HCF.
HCF of 220 and 195 (Euclid’s division algorithm) HCF of 429 and 154 (Euclid’s division algorithm) HCF of 846 and 504 (Euclid’s division algorithm) HCF of 665 and 105 (Euclid’s division algorithm) HCF of 552 and 324 (Euclid’s division algorithm) HCF of 714 and 350 (Euclid’s division algorithm) HCF of 580 and 420 (Euclid’s division algorithm) HCF of 552 and 336 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
5 11 18 35 12 14 20 24 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 63
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 440. One number is 88. Find the other. HCF of two numbers is 4 and their LCM is 140. One number is 20. Find the other. HCF of two numbers is 5 and their LCM is 220. One number is 20. Find the other. HCF of two numbers is 7 and their LCM is 294. One number is 42. Find the other. HCF of two numbers is 2 and their LCM is 80. One number is 10. Find the other. HCF of two numbers is 13 and their LCM is 78. One number is 39. Find the other.
✅ Answer key — HCF × LCM = product
55 28 55 49 16 26 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 63
Name: Date: Score: / 8
Answer without long division.
Does 63/200 have a terminating decimal expansion? Does 32/125 have a terminating decimal expansion? Does 517/400 have a terminating decimal expansion? Does 47/50 have a terminating decimal expansion? Does 128/125 have a terminating decimal expansion? Does 156/55 have a terminating decimal expansion? Does 43/16 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 5³) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 2) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 63
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √90 Rational or irrational: √83 Rational or irrational: 5√74 Rational or irrational: √33 Rational or irrational: 1 + √21 Rational or irrational: √84 Rational or irrational: 9 + √20 Rational or irrational: 9√71 Rational or irrational: 7 + √51 Rational or irrational: 5√39 Rational or irrational: 2√20 Rational or irrational: 9√18
✅ 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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