Free · Class 10 · 6 worksheets · answer keys · practise online · set 72
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 72
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2800 Prime factorisation of 1444 Prime factorisation of 711 Prime factorisation of 988 Prime factorisation of 2795 Prime factorisation of 968 Prime factorisation of 747 Prime factorisation of 1456 Prime factorisation of 236 Prime factorisation of 364
✅ Answer key — Prime factorisation
2⁴ × 5² × 7 2² × 19² 3² × 79 2² × 13 × 19 5 × 13 × 43 2³ × 11² 3² × 83 2⁴ × 7 × 13 2² × 59 2² × 7 × 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 72
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 20 and 48 HCF and LCM of 36 and 198 HCF and LCM of 108 and 120 HCF and LCM of 28 and 210 HCF and LCM of 27 and 30 HCF and LCM of 25 and 35 HCF and LCM of 28 and 32 HCF and LCM of 208 and 224
✅ Answer key — HCF and LCM
HCF = 4, LCM = 240 HCF = 18, LCM = 396 HCF = 12, LCM = 1080 HCF = 14, LCM = 420 HCF = 3, LCM = 270 HCF = 5, LCM = 175 HCF = 4, LCM = 224 HCF = 16, LCM = 2912 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 72
Name: Date: Score: / 8
Find the HCF.
HCF of 378 and 329 (Euclid’s division algorithm) HCF of 273 and 112 (Euclid’s division algorithm) HCF of 448 and 176 (Euclid’s division algorithm) HCF of 470 and 410 (Euclid’s division algorithm) HCF of 512 and 464 (Euclid’s division algorithm) HCF of 575 and 200 (Euclid’s division algorithm) HCF of 638 and 451 (Euclid’s division algorithm) HCF of 675 and 325 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
7 7 16 10 16 25 11 25 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 72
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 390. One number is 130. Find the other. HCF of two numbers is 3 and their LCM is 120. One number is 15. Find the other. HCF of two numbers is 7 and their LCM is 539. One number is 49. Find the other. HCF of two numbers is 3 and their LCM is 108. One number is 12. Find the other. HCF of two numbers is 7 and their LCM is 420. One number is 84. Find the other. HCF of two numbers is 12 and their LCM is 396. One number is 132. Find the other.
✅ Answer key — HCF × LCM = product
39 24 77 27 35 36 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 72
Name: Date: Score: / 8
Answer without long division.
Does 411/625 have a terminating decimal expansion? Does 3/10 have a terminating decimal expansion? Does 187/70 have a terminating decimal expansion? Does 549/1040 have a terminating decimal expansion? Does 31/15 have a terminating decimal expansion? Does 109/40 have a terminating decimal expansion? Does 61/26 have a terminating decimal expansion? Does 17/8 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2 × 5) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2³ × 5) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 2³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 72
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9√82 Rational or irrational: √87 Rational or irrational: 2 + √17 Rational or irrational: 3√23 Rational or irrational: 2√71 Rational or irrational: 7 + √75 Rational or irrational: √12 Rational or irrational: √22 Rational or irrational: 7 + √43 Rational or irrational: √8 Rational or irrational: √62 Rational or irrational: √15
✅ 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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