Free · Class 10 · 6 worksheets · answer keys · practise online · set 19
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 19
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 423 Prime factorisation of 2997 Prime factorisation of 1995 Prime factorisation of 2440 Prime factorisation of 650 Prime factorisation of 2142 Prime factorisation of 2774 Prime factorisation of 1791 Prime factorisation of 627 Prime factorisation of 1020
✅ Answer key — Prime factorisation
3² × 47 3⁴ × 37 3 × 5 × 7 × 19 2³ × 5 × 61 2 × 5² × 13 2 × 3² × 7 × 17 2 × 19 × 73 3² × 199 3 × 11 × 19 2² × 3 × 5 × 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 19
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 54 and 99 HCF and LCM of 9 and 33 HCF and LCM of 16 and 60 HCF and LCM of 32 and 112 HCF and LCM of 20 and 150 HCF and LCM of 6 and 39 HCF and LCM of 6 and 20 HCF and LCM of 20 and 32
✅ Answer key — HCF and LCM
HCF = 9, LCM = 594 HCF = 3, LCM = 99 HCF = 4, LCM = 240 HCF = 16, LCM = 224 HCF = 10, LCM = 300 HCF = 3, LCM = 78 HCF = 2, LCM = 60 HCF = 4, LCM = 160 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 19
Name: Date: Score: / 8
Find the HCF.
HCF of 870 and 551 (Euclid’s division algorithm) HCF of 612 and 576 (Euclid’s division algorithm) HCF of 176 and 154 (Euclid’s division algorithm) HCF of 324 and 189 (Euclid’s division algorithm) HCF of 507 and 286 (Euclid’s division algorithm) HCF of 258 and 240 (Euclid’s division algorithm) HCF of 475 and 247 (Euclid’s division algorithm) HCF of 285 and 220 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
29 36 22 27 13 6 19 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 19
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 273. One number is 39. Find the other. HCF of two numbers is 8 and their LCM is 448. One number is 64. Find the other. HCF of two numbers is 9 and their LCM is 693. One number is 99. Find the other. HCF of two numbers is 7 and their LCM is 588. One number is 49. Find the other. HCF of two numbers is 8 and their LCM is 704. One number is 88. Find the other. HCF of two numbers is 12 and their LCM is 168. One number is 84. Find the other.
✅ Answer key — HCF × LCM = product
91 56 63 84 64 24 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 19
Name: Date: Score: / 8
Answer without long division.
Does 388/275 have a terminating decimal expansion? Does 197/100 have a terminating decimal expansion? Does 233/125 have a terminating decimal expansion? Does 84/55 have a terminating decimal expansion? Does 164/55 have a terminating decimal expansion? Does 14/55 have a terminating decimal expansion? Does 1639/625 have a terminating decimal expansion? Does 2173/750 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 19
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √42 Rational or irrational: 2√89 Rational or irrational: √29 Rational or irrational: 2 + √59 Rational or irrational: √68 Rational or irrational: 4√30 Rational or irrational: 3 + √66 Rational or irrational: √13 Rational or irrational: √58 Rational or irrational: 5 + √61 Rational or irrational: √35 Rational or irrational: √98
✅ 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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