Free · Class 10 · 6 worksheets · answer keys · practise online · set 56
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 56
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1251 Prime factorisation of 1852 Prime factorisation of 120 Prime factorisation of 2224 Prime factorisation of 1845 Prime factorisation of 2754 Prime factorisation of 897 Prime factorisation of 2366 Prime factorisation of 1593 Prime factorisation of 168
✅ Answer key — Prime factorisation
3² × 139 2² × 463 2³ × 3 × 5 2⁴ × 139 3² × 5 × 41 2 × 3⁴ × 17 3 × 13 × 23 2 × 7 × 13² 3³ × 59 2³ × 3 × 7 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 56
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 119 and 187 HCF and LCM of 8 and 22 HCF and LCM of 50 and 120 HCF and LCM of 20 and 25 HCF and LCM of 63 and 135 HCF and LCM of 42 and 154 HCF and LCM of 12 and 28 HCF and LCM of 48 and 78
✅ Answer key — HCF and LCM
HCF = 17, LCM = 1309 HCF = 2, LCM = 88 HCF = 10, LCM = 600 HCF = 5, LCM = 100 HCF = 9, LCM = 945 HCF = 14, LCM = 462 HCF = 4, LCM = 84 HCF = 6, LCM = 624 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 56
Name: Date: Score: / 8
Find the HCF.
HCF of 434 and 350 (Euclid’s division algorithm) HCF of 378 and 273 (Euclid’s division algorithm) HCF of 198 and 187 (Euclid’s division algorithm) HCF of 630 and 150 (Euclid’s division algorithm) HCF of 114 and 110 (Euclid’s division algorithm) HCF of 648 and 528 (Euclid’s division algorithm) HCF of 825 and 500 (Euclid’s division algorithm) HCF of 232 and 120 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
14 21 11 30 2 24 25 8 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 56
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 84. One number is 12. Find the other. HCF of two numbers is 13 and their LCM is 312. One number is 104. Find the other. HCF of two numbers is 11 and their LCM is 462. One number is 66. Find the other. HCF of two numbers is 10 and their LCM is 240. One number is 80. Find the other. HCF of two numbers is 2 and their LCM is 66. One number is 22. Find the other. HCF of two numbers is 11 and their LCM is 1452. One number is 132. Find the other.
✅ Answer key — HCF × LCM = product
14 39 77 30 6 121 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 56
Name: Date: Score: / 8
Answer without long division.
Does 31/22 have a terminating decimal expansion? Does 7/4 have a terminating decimal expansion? Does 58/35 have a terminating decimal expansion? Does 251/275 have a terminating decimal expansion? Does 633/560 have a terminating decimal expansion? Does 509/400 have a terminating decimal expansion? Does 2576/1875 have a terminating decimal expansion? Does 86/55 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 56
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √17 Rational or irrational: √19 Rational or irrational: 8 + √83 Rational or irrational: √98 Rational or irrational: 1√17 Rational or irrational: √21 Rational or irrational: 4√37 Rational or irrational: √54 Rational or irrational: √36 Rational or irrational: 4 + √41 Rational or irrational: √94 Rational or irrational: √59
✅ 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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