Free · Class 10 · 6 worksheets · answer keys · practise online · set 62
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 62
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 494 Prime factorisation of 2936 Prime factorisation of 2996 Prime factorisation of 1605 Prime factorisation of 1800 Prime factorisation of 950 Prime factorisation of 996 Prime factorisation of 2805 Prime factorisation of 2064 Prime factorisation of 174
✅ Answer key — Prime factorisation
2 × 13 × 19 2³ × 367 2² × 7 × 107 3 × 5 × 107 2³ × 3² × 5² 2 × 5² × 19 2² × 3 × 83 3 × 5 × 11 × 17 2⁴ × 3 × 43 2 × 3 × 29 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 62
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 81 and 99 HCF and LCM of 105 and 150 HCF and LCM of 38 and 171 HCF and LCM of 12 and 39 HCF and LCM of 143 and 154 HCF and LCM of 176 and 240 HCF and LCM of 90 and 234 HCF and LCM of 154 and 168
✅ Answer key — HCF and LCM
HCF = 9, LCM = 891 HCF = 15, LCM = 1050 HCF = 19, LCM = 342 HCF = 3, LCM = 156 HCF = 11, LCM = 2002 HCF = 16, LCM = 2640 HCF = 18, LCM = 1170 HCF = 14, LCM = 1848 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 62
Name: Date: Score: / 8
Find the HCF.
HCF of 212 and 184 (Euclid’s division algorithm) HCF of 840 and 375 (Euclid’s division algorithm) HCF of 680 and 527 (Euclid’s division algorithm) HCF of 602 and 420 (Euclid’s division algorithm) HCF of 555 and 210 (Euclid’s division algorithm) HCF of 560 and 126 (Euclid’s division algorithm) HCF of 868 and 279 (Euclid’s division algorithm) HCF of 651 and 378 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
4 15 17 14 15 14 31 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 62
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 792. One number is 88. Find the other. HCF of two numbers is 7 and their LCM is 98. One number is 14. Find the other. HCF of two numbers is 10 and their LCM is 350. One number is 70. Find the other. HCF of two numbers is 9 and their LCM is 189. One number is 27. Find the other. HCF of two numbers is 14 and their LCM is 1232. One number is 112. Find the other. HCF of two numbers is 6 and their LCM is 144. One number is 18. Find the other.
✅ Answer key — HCF × LCM = product
72 49 50 63 154 48 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 62
Name: Date: Score: / 8
Answer without long division.
Does 183/80 have a terminating decimal expansion? Does 6/5 have a terminating decimal expansion? Does 531/260 have a terminating decimal expansion? Does 53/60 have a terminating decimal expansion? Does 14/25 have a terminating decimal expansion? Does 139/75 have a terminating decimal expansion? Does 113/1250 have a terminating decimal expansion? Does 1399/625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 5⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 62
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 5√16 Rational or irrational: 7 + √47 Rational or irrational: √28 Rational or irrational: √71 Rational or irrational: 7√17 Rational or irrational: 6√38 Rational or irrational: 6 + √15 Rational or irrational: 1 + √57 Rational or irrational: 9 + √95 Rational or irrational: 1 + √77 Rational or irrational: 3√4 Rational or irrational: 8√49
✅ Answer key — Rational or irrational?
rational irrational irrational irrational irrational irrational irrational irrational irrational irrational rational rational 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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