Free · Class 10 · 6 worksheets · answer keys · practise online · set 20
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 20
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 375 Prime factorisation of 2824 Prime factorisation of 530 Prime factorisation of 378 Prime factorisation of 2328 Prime factorisation of 963 Prime factorisation of 255 Prime factorisation of 248 Prime factorisation of 988 Prime factorisation of 294
✅ Answer key — Prime factorisation
3 × 5³ 2³ × 353 2 × 5 × 53 2 × 3³ × 7 2³ × 3 × 97 3² × 107 3 × 5 × 17 2³ × 31 2² × 13 × 19 2 × 3 × 7² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 20
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 200 and 260 HCF and LCM of 12 and 56 HCF and LCM of 135 and 150 HCF and LCM of 30 and 105 HCF and LCM of 40 and 130 HCF and LCM of 60 and 108 HCF and LCM of 88 and 104 HCF and LCM of 119 and 187
✅ Answer key — HCF and LCM
HCF = 20, LCM = 2600 HCF = 4, LCM = 168 HCF = 15, LCM = 1350 HCF = 15, LCM = 210 HCF = 10, LCM = 520 HCF = 12, LCM = 540 HCF = 8, LCM = 1144 HCF = 17, LCM = 1309 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 20
Name: Date: Score: / 8
Find the HCF.
HCF of 468 and 120 (Euclid’s division algorithm) HCF of 188 and 124 (Euclid’s division algorithm) HCF of 558 and 288 (Euclid’s division algorithm) HCF of 910 and 338 (Euclid’s division algorithm) HCF of 336 and 138 (Euclid’s division algorithm) HCF of 392 and 120 (Euclid’s division algorithm) HCF of 590 and 490 (Euclid’s division algorithm) HCF of 616 and 506 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
12 4 18 26 6 8 10 22 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 20
Name: Date: Score: / 6
Solve.
HCF of two numbers is 15 and their LCM is 225. One number is 45. Find the other. HCF of two numbers is 11 and their LCM is 1210. One number is 121. Find the other. HCF of two numbers is 3 and their LCM is 270. One number is 30. Find the other. HCF of two numbers is 11 and their LCM is 495. One number is 55. Find the other. HCF of two numbers is 11 and their LCM is 847. One number is 77. Find the other. HCF of two numbers is 11 and their LCM is 66. One number is 22. Find the other.
✅ Answer key — HCF × LCM = product
75 110 27 99 121 33 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 20
Name: Date: Score: / 8
Answer without long division.
Does 1/2 have a terminating decimal expansion? Does 128/55 have a terminating decimal expansion? Does 334/125 have a terminating decimal expansion? Does 131/400 have a terminating decimal expansion? Does 2963/1250 have a terminating decimal expansion? Does 99/560 have a terminating decimal expansion? Does 139/100 have a terminating decimal expansion? Does 25/22 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5³) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5²) 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 20
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 3 + √44 Rational or irrational: 5 + √16 Rational or irrational: √84 Rational or irrational: √66 Rational or irrational: 7 + √83 Rational or irrational: √37 Rational or irrational: √38 Rational or irrational: √53 Rational or irrational: √40 Rational or irrational: 5√31 Rational or irrational: 8√22 Rational or irrational: 1√45
✅ Answer key — Rational or irrational?
irrational rational 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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