Free · Class 10 · 6 worksheets · answer keys · practise online · set 4
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 4
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 402 Prime factorisation of 1338 Prime factorisation of 2008 Prime factorisation of 2546 Prime factorisation of 2496 Prime factorisation of 2500 Prime factorisation of 1778 Prime factorisation of 243 Prime factorisation of 1479 Prime factorisation of 664
✅ Answer key — Prime factorisation
2 × 3 × 67 2 × 3 × 223 2³ × 251 2 × 19 × 67 2⁶ × 3 × 13 2² × 5⁴ 2 × 7 × 127 3⁵ 3 × 17 × 29 2³ × 83 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 4
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 84 and 90 HCF and LCM of 56 and 91 HCF and LCM of 60 and 168 HCF and LCM of 16 and 44 HCF and LCM of 48 and 52 HCF and LCM of 85 and 136 HCF and LCM of 70 and 84 HCF and LCM of 75 and 120
✅ Answer key — HCF and LCM
HCF = 6, LCM = 1260 HCF = 7, LCM = 728 HCF = 12, LCM = 840 HCF = 4, LCM = 176 HCF = 4, LCM = 624 HCF = 17, LCM = 680 HCF = 14, LCM = 420 HCF = 15, LCM = 600 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 4
Name: Date: Score: / 8
Find the HCF.
HCF of 235 and 170 (Euclid’s division algorithm) HCF of 234 and 228 (Euclid’s division algorithm) HCF of 378 and 243 (Euclid’s division algorithm) HCF of 860 and 680 (Euclid’s division algorithm) HCF of 754 and 624 (Euclid’s division algorithm) HCF of 361 and 209 (Euclid’s division algorithm) HCF of 240 and 132 (Euclid’s division algorithm) HCF of 378 and 105 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
5 6 27 20 26 19 12 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 4
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 18. One number is 6. Find the other. HCF of two numbers is 14 and their LCM is 392. One number is 98. Find the other. HCF of two numbers is 10 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 2 and their LCM is 56. One number is 14. Find the other. HCF of two numbers is 5 and their LCM is 30. One number is 15. Find the other. HCF of two numbers is 14 and their LCM is 392. One number is 56. Find the other.
✅ Answer key — HCF × LCM = product
9 56 70 8 10 98 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 4
Name: Date: Score: / 8
Answer without long division.
Does 6/5 have a terminating decimal expansion? Does 941/520 have a terminating decimal expansion? Does 23/10 have a terminating decimal expansion? Does 43/80 have a terminating decimal expansion? Does 2923/1250 have a terminating decimal expansion? Does 1514/625 have a terminating decimal expansion? Does 1023/625 have a terminating decimal expansion? Does 2/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 4
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √80 Rational or irrational: 6 + √62 Rational or irrational: 9 + √83 Rational or irrational: 4 + √2 Rational or irrational: 3√58 Rational or irrational: √92 Rational or irrational: √13 Rational or irrational: 9√11 Rational or irrational: 3 + √38 Rational or irrational: 2 + √46 Rational or irrational: 3 + √72 Rational or irrational: 1√48
✅ 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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