Free · Class 10 · 6 worksheets · answer keys · practise online · set 71
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 71
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2684 Prime factorisation of 1686 Prime factorisation of 910 Prime factorisation of 1869 Prime factorisation of 2220 Prime factorisation of 2054 Prime factorisation of 2082 Prime factorisation of 2472 Prime factorisation of 675 Prime factorisation of 176
✅ Answer key — Prime factorisation
2² × 11 × 61 2 × 3 × 281 2 × 5 × 7 × 13 3 × 7 × 89 2² × 3 × 5 × 37 2 × 13 × 79 2 × 3 × 347 2³ × 3 × 103 3³ × 5² 2⁴ × 11 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 71
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 30 and 66 HCF and LCM of 98 and 105 HCF and LCM of 80 and 104 HCF and LCM of 152 and 247 HCF and LCM of 27 and 42 HCF and LCM of 84 and 182 HCF and LCM of 132 and 180 HCF and LCM of 40 and 150
✅ Answer key — HCF and LCM
HCF = 6, LCM = 330 HCF = 7, LCM = 1470 HCF = 8, LCM = 1040 HCF = 19, LCM = 1976 HCF = 3, LCM = 378 HCF = 14, LCM = 1092 HCF = 12, LCM = 1980 HCF = 10, LCM = 600 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 71
Name: Date: Score: / 8
Find the HCF.
HCF of 588 and 360 (Euclid’s division algorithm) HCF of 234 and 228 (Euclid’s division algorithm) HCF of 744 and 528 (Euclid’s division algorithm) HCF of 798 and 273 (Euclid’s division algorithm) HCF of 814 and 374 (Euclid’s division algorithm) HCF of 988 and 874 (Euclid’s division algorithm) HCF of 867 and 731 (Euclid’s division algorithm) HCF of 992 and 960 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
12 6 24 21 22 38 17 32 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 71
Name: Date: Score: / 6
Solve.
HCF of two numbers is 4 and their LCM is 396. One number is 44. Find the other. HCF of two numbers is 8 and their LCM is 504. One number is 56. Find the other. HCF of two numbers is 14 and their LCM is 1260. One number is 126. Find the other. HCF of two numbers is 13 and their LCM is 858. One number is 143. Find the other. HCF of two numbers is 11 and their LCM is 132. One number is 33. Find the other. HCF of two numbers is 13 and their LCM is 390. One number is 65. Find the other.
✅ Answer key — HCF × LCM = product
36 72 140 78 44 78 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 71
Name: Date: Score: / 8
Answer without long division.
Does 131/80 have a terminating decimal expansion? Does 889/500 have a terminating decimal expansion? Does 389/520 have a terminating decimal expansion? Does 1194/625 have a terminating decimal expansion? Does 113/100 have a terminating decimal expansion? Does 101/40 have a terminating decimal expansion? Does 3802/1375 have a terminating decimal expansion? Does 44/25 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 71
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √40 Rational or irrational: √69 Rational or irrational: √52 Rational or irrational: 8√37 Rational or irrational: √72 Rational or irrational: 6 + √52 Rational or irrational: 8 + √60 Rational or irrational: √56 Rational or irrational: 6√81 Rational or irrational: 3 + √96 Rational or irrational: 3 + √27 Rational or irrational: 6 + √54
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational rational 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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