Free · Class 10 · 6 worksheets · answer keys · practise online · set 22
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 22
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1576 Prime factorisation of 1716 Prime factorisation of 2678 Prime factorisation of 1736 Prime factorisation of 1083 Prime factorisation of 1085 Prime factorisation of 374 Prime factorisation of 582 Prime factorisation of 1809 Prime factorisation of 1758
✅ Answer key — Prime factorisation
2³ × 197 2² × 3 × 11 × 13 2 × 13 × 103 2³ × 7 × 31 3 × 19² 5 × 7 × 31 2 × 11 × 17 2 × 3 × 97 3³ × 67 2 × 3 × 293 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 22
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 57 and 190 HCF and LCM of 18 and 24 HCF and LCM of 120 and 260 HCF and LCM of 105 and 150 HCF and LCM of 48 and 176 HCF and LCM of 126 and 196 HCF and LCM of 76 and 247 HCF and LCM of 70 and 77
✅ Answer key — HCF and LCM
HCF = 19, LCM = 570 HCF = 6, LCM = 72 HCF = 20, LCM = 1560 HCF = 15, LCM = 1050 HCF = 16, LCM = 528 HCF = 14, LCM = 1764 HCF = 19, LCM = 988 HCF = 7, LCM = 770 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 22
Name: Date: Score: / 8
Find the HCF.
HCF of 130 and 110 (Euclid’s division algorithm) HCF of 910 and 858 (Euclid’s division algorithm) HCF of 810 and 198 (Euclid’s division algorithm) HCF of 713 and 403 (Euclid’s division algorithm) HCF of 700 and 574 (Euclid’s division algorithm) HCF of 590 and 340 (Euclid’s division algorithm) HCF of 459 and 441 (Euclid’s division algorithm) HCF of 195 and 190 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
10 26 18 31 14 10 9 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 22
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 280. One number is 70. Find the other. HCF of two numbers is 7 and their LCM is 252. One number is 63. Find the other. HCF of two numbers is 14 and their LCM is 560. One number is 70. Find the other. HCF of two numbers is 14 and their LCM is 1176. One number is 168. Find the other. HCF of two numbers is 2 and their LCM is 48. One number is 6. Find the other. HCF of two numbers is 9 and their LCM is 54. One number is 18. Find the other.
✅ Answer key — HCF × LCM = product
40 28 112 98 16 27 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 22
Name: Date: Score: / 8
Answer without long division.
Does 49/40 have a terminating decimal expansion? Does 61/22 have a terminating decimal expansion? Does 21/8 have a terminating decimal expansion? Does 2049/1250 have a terminating decimal expansion? Does 1076/375 have a terminating decimal expansion? Does 1/5 have a terminating decimal expansion? Does 451/200 have a terminating decimal expansion? Does 23/10 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2³) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2 × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 22
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √91 Rational or irrational: √95 Rational or irrational: 8 + √57 Rational or irrational: √59 Rational or irrational: 4√20 Rational or irrational: 4√80 Rational or irrational: 5 + √74 Rational or irrational: 9 + √25 Rational or irrational: 4 + √3 Rational or irrational: 5 + √35 Rational or irrational: √10 Rational or irrational: 1√53
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational rational 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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