Free · Class 10 · 6 worksheets · answer keys · practise online · set 48
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 48
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 938 Prime factorisation of 1424 Prime factorisation of 1468 Prime factorisation of 2345 Prime factorisation of 1647 Prime factorisation of 1584 Prime factorisation of 2145 Prime factorisation of 1278 Prime factorisation of 1916 Prime factorisation of 318
✅ Answer key — Prime factorisation
2 × 7 × 67 2⁴ × 89 2² × 367 5 × 7 × 67 3³ × 61 2⁴ × 3² × 11 3 × 5 × 11 × 13 2 × 3² × 71 2² × 479 2 × 3 × 53 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 48
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 104 and 117 HCF and LCM of 21 and 30 HCF and LCM of 36 and 156 HCF and LCM of 84 and 144 HCF and LCM of 15 and 39 HCF and LCM of 48 and 176 HCF and LCM of 20 and 36 HCF and LCM of 135 and 150
✅ Answer key — HCF and LCM
HCF = 13, LCM = 936 HCF = 3, LCM = 210 HCF = 12, LCM = 468 HCF = 12, LCM = 1008 HCF = 3, LCM = 195 HCF = 16, LCM = 528 HCF = 4, LCM = 180 HCF = 15, LCM = 1350 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 48
Name: Date: Score: / 8
Find the HCF.
HCF of 246 and 198 (Euclid’s division algorithm) HCF of 185 and 111 (Euclid’s division algorithm) HCF of 624 and 544 (Euclid’s division algorithm) HCF of 792 and 429 (Euclid’s division algorithm) HCF of 585 and 104 (Euclid’s division algorithm) HCF of 650 and 425 (Euclid’s division algorithm) HCF of 988 and 390 (Euclid’s division algorithm) HCF of 266 and 112 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
6 37 16 33 13 25 26 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 48
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 780. One number is 65. Find the other. HCF of two numbers is 5 and their LCM is 120. One number is 15. Find the other. HCF of two numbers is 12 and their LCM is 168. One number is 84. Find the other. HCF of two numbers is 15 and their LCM is 600. One number is 75. Find the other. HCF of two numbers is 11 and their LCM is 220. One number is 55. Find the other. HCF of two numbers is 11 and their LCM is 154. One number is 22. Find the other.
✅ Answer key — HCF × LCM = product
156 40 24 120 44 77 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 48
Name: Date: Score: / 8
Answer without long division.
Does 3/2 have a terminating decimal expansion? Does 226/125 have a terminating decimal expansion? Does 1/2 have a terminating decimal expansion? Does 3/16 have a terminating decimal expansion? Does 88/35 have a terminating decimal expansion? Does 41/50 have a terminating decimal expansion? Does 23/25 have a terminating decimal expansion? Does 93/70 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) Yes — terminating (denominator 5³) Yes — terminating (denominator 2) Yes — terminating (denominator 2⁴) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 7) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 48
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √82 Rational or irrational: 8 + √89 Rational or irrational: 3√89 Rational or irrational: 1 + √62 Rational or irrational: √57 Rational or irrational: 2√15 Rational or irrational: 5 + √71 Rational or irrational: 7√50 Rational or irrational: 1√27 Rational or irrational: 6√15 Rational or irrational: √87 Rational or irrational: √83
✅ 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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