Free · Class 10 · 6 worksheets · answer keys · practise online · set 31
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 31
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2877 Prime factorisation of 1962 Prime factorisation of 1076 Prime factorisation of 1928 Prime factorisation of 2303 Prime factorisation of 1488 Prime factorisation of 2800 Prime factorisation of 1988 Prime factorisation of 882 Prime factorisation of 2278
✅ Answer key — Prime factorisation
3 × 7 × 137 2 × 3² × 109 2² × 269 2³ × 241 7² × 47 2⁴ × 3 × 31 2⁴ × 5² × 7 2² × 7 × 71 2 × 3² × 7² 2 × 17 × 67 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 31
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 42 and 77 HCF and LCM of 40 and 75 HCF and LCM of 32 and 44 HCF and LCM of 33 and 45 HCF and LCM of 57 and 266 HCF and LCM of 45 and 50 HCF and LCM of 104 and 195 HCF and LCM of 154 and 182
✅ Answer key — HCF and LCM
HCF = 7, LCM = 462 HCF = 5, LCM = 600 HCF = 4, LCM = 352 HCF = 3, LCM = 495 HCF = 19, LCM = 798 HCF = 5, LCM = 450 HCF = 13, LCM = 1560 HCF = 14, LCM = 2002 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 31
Name: Date: Score: / 8
Find the HCF.
HCF of 760 and 703 (Euclid’s division algorithm) HCF of 275 and 253 (Euclid’s division algorithm) HCF of 828 and 288 (Euclid’s division algorithm) HCF of 481 and 370 (Euclid’s division algorithm) HCF of 576 and 522 (Euclid’s division algorithm) HCF of 800 and 340 (Euclid’s division algorithm) HCF of 903 and 693 (Euclid’s division algorithm) HCF of 680 and 357 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
19 11 36 37 18 20 21 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 31
Name: Date: Score: / 6
Solve.
HCF of two numbers is 7 and their LCM is 70. One number is 35. Find the other. HCF of two numbers is 6 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 15 and their LCM is 945. One number is 105. Find the other. HCF of two numbers is 15 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 14 and their LCM is 1078. One number is 98. Find the other. HCF of two numbers is 4 and their LCM is 132. One number is 44. Find the other.
✅ Answer key — HCF × LCM = product
14 30 135 105 154 12 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 31
Name: Date: Score: / 8
Answer without long division.
Does 74/35 have a terminating decimal expansion? Does 53/22 have a terminating decimal expansion? Does 637/500 have a terminating decimal expansion? Does 13/44 have a terminating decimal expansion? Does 507/400 have a terminating decimal expansion? Does 567/550 have a terminating decimal expansion? Does 29/56 have a terminating decimal expansion? Does 2707/1250 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 31
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9√76 Rational or irrational: √46 Rational or irrational: 2 + √68 Rational or irrational: 5 + √25 Rational or irrational: 5 + √99 Rational or irrational: √22 Rational or irrational: 2√9 Rational or irrational: 6√85 Rational or irrational: 7 + √46 Rational or irrational: 2 + √92 Rational or irrational: 4 + √41 Rational or irrational: 3 + √82
✅ Answer key — Rational or irrational?
irrational irrational irrational rational irrational irrational rational 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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