Free · Class 10 · 6 worksheets · answer keys · practise online · set 82
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 82
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1330 Prime factorisation of 1776 Prime factorisation of 642 Prime factorisation of 540 Prime factorisation of 1971 Prime factorisation of 1521 Prime factorisation of 2502 Prime factorisation of 1296 Prime factorisation of 908 Prime factorisation of 1952
✅ Answer key — Prime factorisation
2 × 5 × 7 × 19 2⁴ × 3 × 37 2 × 3 × 107 2² × 3³ × 5 3³ × 73 3² × 13² 2 × 3² × 139 2⁴ × 3⁴ 2² × 227 2⁵ × 61 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 82
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 60 and 66 HCF and LCM of 42 and 49 HCF and LCM of 39 and 52 HCF and LCM of 48 and 88 HCF and LCM of 85 and 204 HCF and LCM of 32 and 104 HCF and LCM of 187 and 238 HCF and LCM of 22 and 55
✅ Answer key — HCF and LCM
HCF = 6, LCM = 660 HCF = 7, LCM = 294 HCF = 13, LCM = 156 HCF = 8, LCM = 528 HCF = 17, LCM = 1020 HCF = 8, LCM = 416 HCF = 17, LCM = 2618 HCF = 11, LCM = 110 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 82
Name: Date: Score: / 8
Find the HCF.
HCF of 144 and 128 (Euclid’s division algorithm) HCF of 396 and 231 (Euclid’s division algorithm) HCF of 512 and 272 (Euclid’s division algorithm) HCF of 609 and 315 (Euclid’s division algorithm) HCF of 720 and 378 (Euclid’s division algorithm) HCF of 374 and 143 (Euclid’s division algorithm) HCF of 672 and 364 (Euclid’s division algorithm) HCF of 779 and 399 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
16 33 16 21 18 11 28 19 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 82
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 231. One number is 33. Find the other. HCF of two numbers is 7 and their LCM is 196. One number is 28. Find the other. HCF of two numbers is 6 and their LCM is 432. One number is 48. Find the other. HCF of two numbers is 13 and their LCM is 572. One number is 52. Find the other. HCF of two numbers is 5 and their LCM is 30. One number is 10. Find the other. HCF of two numbers is 4 and their LCM is 56. One number is 8. Find the other.
✅ Answer key — HCF × LCM = product
77 49 54 143 15 28 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 82
Name: Date: Score: / 8
Answer without long division.
Does 23/15 have a terminating decimal expansion? Does 191/70 have a terminating decimal expansion? Does 283/200 have a terminating decimal expansion? Does 2587/2000 have a terminating decimal expansion? Does 22/25 have a terminating decimal expansion? Does 381/200 have a terminating decimal expansion? Does 13/15 have a terminating decimal expansion? Does 823/550 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 5²) Yes — terminating (denominator 2³ × 5²) No — non-terminating repeating (denominator has the factor 3) No — non-terminating repeating (denominator has the factor 11) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 82
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9 + √95 Rational or irrational: 1 + √39 Rational or irrational: 1√44 Rational or irrational: 9√14 Rational or irrational: 1√86 Rational or irrational: 8 + √80 Rational or irrational: √54 Rational or irrational: √9 Rational or irrational: 8√11 Rational or irrational: √80 Rational or irrational: 4 + √96 Rational or irrational: 4√76
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational rational 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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