Free · Class 10 · 6 worksheets · answer keys · practise online · set 11
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 11
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1794 Prime factorisation of 410 Prime factorisation of 897 Prime factorisation of 2398 Prime factorisation of 2992 Prime factorisation of 2765 Prime factorisation of 1308 Prime factorisation of 474 Prime factorisation of 833 Prime factorisation of 1659
✅ Answer key — Prime factorisation
2 × 3 × 13 × 23 2 × 5 × 41 3 × 13 × 23 2 × 11 × 109 2⁴ × 11 × 17 5 × 7 × 79 2² × 3 × 109 2 × 3 × 79 7² × 17 3 × 7 × 79 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 11
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 144 and 176 HCF and LCM of 36 and 52 HCF and LCM of 12 and 26 HCF and LCM of 10 and 65 HCF and LCM of 20 and 90 HCF and LCM of 12 and 44 HCF and LCM of 112 and 176 HCF and LCM of 18 and 24
✅ Answer key — HCF and LCM
HCF = 16, LCM = 1584 HCF = 4, LCM = 468 HCF = 2, LCM = 156 HCF = 5, LCM = 130 HCF = 10, LCM = 180 HCF = 4, LCM = 132 HCF = 16, LCM = 1232 HCF = 6, LCM = 72 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 11
Name: Date: Score: / 8
Find the HCF.
HCF of 240 and 155 (Euclid’s division algorithm) HCF of 517 and 385 (Euclid’s division algorithm) HCF of 171 and 111 (Euclid’s division algorithm) HCF of 480 and 248 (Euclid’s division algorithm) HCF of 550 and 120 (Euclid’s division algorithm) HCF of 468 and 189 (Euclid’s division algorithm) HCF of 784 and 688 (Euclid’s division algorithm) HCF of 903 and 672 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
5 11 3 8 10 9 16 21 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 11
Name: Date: Score: / 6
Solve.
HCF of two numbers is 10 and their LCM is 300. One number is 30. Find the other. HCF of two numbers is 11 and their LCM is 264. One number is 33. Find the other. HCF of two numbers is 13 and their LCM is 364. One number is 52. Find the other. HCF of two numbers is 7 and their LCM is 630. One number is 70. Find the other. HCF of two numbers is 13 and their LCM is 312. One number is 104. Find the other. HCF of two numbers is 5 and their LCM is 200. One number is 25. Find the other.
✅ Answer key — HCF × LCM = product
100 88 91 63 39 40 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 11
Name: Date: Score: / 8
Answer without long division.
Does 5/2 have a terminating decimal expansion? Does 44/35 have a terminating decimal expansion? Does 129/50 have a terminating decimal expansion? Does 22/25 have a terminating decimal expansion? Does 341/200 have a terminating decimal expansion? Does 4346/1875 have a terminating decimal expansion? Does 1198/625 have a terminating decimal expansion? Does 33/16 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 5²) Yes — terminating (denominator 2³ × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 11
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √71 Rational or irrational: 3√94 Rational or irrational: √88 Rational or irrational: 7√4 Rational or irrational: 4√39 Rational or irrational: √77 Rational or irrational: √33 Rational or irrational: 7 + √64 Rational or irrational: 7 + √42 Rational or irrational: √74 Rational or irrational: 1√25 Rational or irrational: 5 + √32
✅ Answer key — Rational or irrational?
irrational irrational irrational rational irrational irrational irrational rational 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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