Free · Class 10 · 6 worksheets · answer keys · practise online · set 29
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 29
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 228 Prime factorisation of 2278 Prime factorisation of 1880 Prime factorisation of 232 Prime factorisation of 2710 Prime factorisation of 1000 Prime factorisation of 248 Prime factorisation of 364 Prime factorisation of 852 Prime factorisation of 198
✅ Answer key — Prime factorisation
2² × 3 × 19 2 × 17 × 67 2³ × 5 × 47 2³ × 29 2 × 5 × 271 2³ × 5³ 2³ × 31 2² × 7 × 13 2² × 3 × 71 2 × 3² × 11 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 29
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 154 and 210 HCF and LCM of 49 and 56 HCF and LCM of 180 and 198 HCF and LCM of 18 and 99 HCF and LCM of 20 and 22 HCF and LCM of 24 and 44 HCF and LCM of 63 and 99 HCF and LCM of 60 and 75
✅ Answer key — HCF and LCM
HCF = 14, LCM = 2310 HCF = 7, LCM = 392 HCF = 18, LCM = 1980 HCF = 9, LCM = 198 HCF = 2, LCM = 220 HCF = 4, LCM = 264 HCF = 9, LCM = 693 HCF = 15, LCM = 300 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 29
Name: Date: Score: / 8
Find the HCF.
HCF of 968 and 330 (Euclid’s division algorithm) HCF of 984 and 312 (Euclid’s division algorithm) HCF of 387 and 288 (Euclid’s division algorithm) HCF of 459 and 170 (Euclid’s division algorithm) HCF of 480 and 130 (Euclid’s division algorithm) HCF of 990 and 612 (Euclid’s division algorithm) HCF of 930 and 527 (Euclid’s division algorithm) HCF of 990 and 960 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
22 24 9 17 10 18 31 30 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 29
Name: Date: Score: / 6
Solve.
HCF of two numbers is 5 and their LCM is 140. One number is 35. Find the other. HCF of two numbers is 7 and their LCM is 441. One number is 49. Find the other. HCF of two numbers is 7 and their LCM is 924. One number is 84. Find the other. HCF of two numbers is 4 and their LCM is 360. One number is 36. Find the other. HCF of two numbers is 6 and their LCM is 264. One number is 24. Find the other. HCF of two numbers is 11 and their LCM is 924. One number is 77. Find the other.
✅ Answer key — HCF × LCM = product
20 63 77 40 66 132 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 29
Name: Date: Score: / 8
Answer without long division.
Does 1084/375 have a terminating decimal expansion? Does 1416/625 have a terminating decimal expansion? Does 41/25 have a terminating decimal expansion? Does 4687/2000 have a terminating decimal expansion? Does 5/4 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 627/280 have a terminating decimal expansion? Does 161/130 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5²) Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2²) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 13) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 29
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √10 Rational or irrational: √67 Rational or irrational: 7 + √5 Rational or irrational: 6√92 Rational or irrational: √22 Rational or irrational: 2√62 Rational or irrational: 7 + √7 Rational or irrational: √58 Rational or irrational: √88 Rational or irrational: √5 Rational or irrational: 4 + √69 Rational or irrational: 3 + √9
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational irrational rational 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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