Free · Class 10 · 6 worksheets · answer keys · practise online · set 15
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 15
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1218 Prime factorisation of 840 Prime factorisation of 2276 Prime factorisation of 2015 Prime factorisation of 2937 Prime factorisation of 1310 Prime factorisation of 1280 Prime factorisation of 1870 Prime factorisation of 170 Prime factorisation of 2514
✅ Answer key — Prime factorisation
2 × 3 × 7 × 29 2³ × 3 × 5 × 7 2² × 569 5 × 13 × 31 3 × 11 × 89 2 × 5 × 131 2⁸ × 5 2 × 5 × 11 × 17 2 × 5 × 17 2 × 3 × 419 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 15
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 132 and 168 HCF and LCM of 60 and 280 HCF and LCM of 204 and 221 HCF and LCM of 24 and 32 HCF and LCM of 60 and 65 HCF and LCM of 14 and 105 HCF and LCM of 56 and 154 HCF and LCM of 153 and 187
✅ Answer key — HCF and LCM
HCF = 12, LCM = 1848 HCF = 20, LCM = 840 HCF = 17, LCM = 2652 HCF = 8, LCM = 96 HCF = 5, LCM = 780 HCF = 7, LCM = 210 HCF = 14, LCM = 616 HCF = 17, LCM = 1683 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 15
Name: Date: Score: / 8
Find the HCF.
HCF of 735 and 675 (Euclid’s division algorithm) HCF of 885 and 705 (Euclid’s division algorithm) HCF of 532 and 154 (Euclid’s division algorithm) HCF of 704 and 112 (Euclid’s division algorithm) HCF of 472 and 456 (Euclid’s division algorithm) HCF of 742 and 672 (Euclid’s division algorithm) HCF of 572 and 198 (Euclid’s division algorithm) HCF of 333 and 297 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
15 15 14 16 8 14 22 9 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 15
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 14 and their LCM is 924. One number is 84. Find the other. HCF of two numbers is 9 and their LCM is 162. One number is 18. Find the other. HCF of two numbers is 5 and their LCM is 550. One number is 50. Find the other. HCF of two numbers is 6 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 9 and their LCM is 378. One number is 63. Find the other.
✅ Answer key — HCF × LCM = product
10 154 81 55 42 54 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 15
Name: Date: Score: / 8
Answer without long division.
Does 121/200 have a terminating decimal expansion? Does 1/2 have a terminating decimal expansion? Does 101/60 have a terminating decimal expansion? Does 2201/2000 have a terminating decimal expansion? Does 323/260 have a terminating decimal expansion? Does 361/125 have a terminating decimal expansion? Does 47/40 have a terminating decimal expansion? Does 185/104 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5³) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 13) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 15
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 6√8 Rational or irrational: 7 + √61 Rational or irrational: 5 + √60 Rational or irrational: 6 + √75 Rational or irrational: 8 + √68 Rational or irrational: √29 Rational or irrational: 7√70 Rational or irrational: √8 Rational or irrational: 4 + √72 Rational or irrational: 1√91 Rational or irrational: 2√48 Rational or irrational: 9 + √58
✅ 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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