Free · Class 10 · 6 worksheets · answer keys · practise online · set 6
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 6
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 408 Prime factorisation of 2373 Prime factorisation of 632 Prime factorisation of 430 Prime factorisation of 1054 Prime factorisation of 2619 Prime factorisation of 575 Prime factorisation of 2871 Prime factorisation of 1914 Prime factorisation of 1786
✅ Answer key — Prime factorisation
2³ × 3 × 17 3 × 7 × 113 2³ × 79 2 × 5 × 43 2 × 17 × 31 3³ × 97 5² × 23 3² × 11 × 29 2 × 3 × 11 × 29 2 × 19 × 47 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 6
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 56 and 182 HCF and LCM of 72 and 135 HCF and LCM of 180 and 200 HCF and LCM of 209 and 247 HCF and LCM of 6 and 14 HCF and LCM of 36 and 45 HCF and LCM of 56 and 154 HCF and LCM of 16 and 104
✅ Answer key — HCF and LCM
HCF = 14, LCM = 728 HCF = 9, LCM = 1080 HCF = 20, LCM = 1800 HCF = 19, LCM = 2717 HCF = 2, LCM = 42 HCF = 9, LCM = 180 HCF = 14, LCM = 616 HCF = 8, LCM = 208 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 6
Name: Date: Score: / 8
Find the HCF.
HCF of 990 and 324 (Euclid’s division algorithm) HCF of 435 and 180 (Euclid’s division algorithm) HCF of 451 and 352 (Euclid’s division algorithm) HCF of 783 and 290 (Euclid’s division algorithm) HCF of 570 and 340 (Euclid’s division algorithm) HCF of 952 and 646 (Euclid’s division algorithm) HCF of 260 and 210 (Euclid’s division algorithm) HCF of 200 and 156 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
18 15 11 29 10 34 10 4 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 6
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 660. One number is 110. Find the other. HCF of two numbers is 11 and their LCM is 693. One number is 77. Find the other. HCF of two numbers is 11 and their LCM is 440. One number is 55. Find the other. HCF of two numbers is 5 and their LCM is 280. One number is 35. Find the other. HCF of two numbers is 3 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 6 and their LCM is 540. One number is 60. Find the other.
✅ Answer key — HCF × LCM = product
60 99 88 40 21 54 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 6
Name: Date: Score: / 8
Answer without long division.
Does 211/140 have a terminating decimal expansion? Does 53/40 have a terminating decimal expansion? Does 7/6 have a terminating decimal expansion? Does 71/25 have a terminating decimal expansion? Does 4759/2000 have a terminating decimal expansion? Does 1/100 have a terminating decimal expansion? Does 142/175 have a terminating decimal expansion? Does 277/100 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5²) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2² × 5²) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5²) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 6
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √93 Rational or irrational: 3√81 Rational or irrational: 9√55 Rational or irrational: 1√83 Rational or irrational: 1 + √33 Rational or irrational: 9√97 Rational or irrational: 2√88 Rational or irrational: 2 + √8 Rational or irrational: 6√35 Rational or irrational: 9√61 Rational or irrational: √25 Rational or irrational: 6 + √43
✅ Answer key — Rational or irrational?
irrational rational irrational irrational irrational irrational irrational irrational irrational irrational rational 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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