Free · Class 10 · 6 worksheets · answer keys · practise online · set 37
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 37
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2410 Prime factorisation of 182 Prime factorisation of 456 Prime factorisation of 1662 Prime factorisation of 2694 Prime factorisation of 268 Prime factorisation of 2968 Prime factorisation of 168 Prime factorisation of 2873 Prime factorisation of 1898
✅ Answer key — Prime factorisation
2 × 5 × 241 2 × 7 × 13 2³ × 3 × 19 2 × 3 × 277 2 × 3 × 449 2² × 67 2³ × 7 × 53 2³ × 3 × 7 13² × 17 2 × 13 × 73 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 37
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 64 and 104 HCF and LCM of 81 and 126 HCF and LCM of 60 and 100 HCF and LCM of 28 and 49 HCF and LCM of 90 and 99 HCF and LCM of 39 and 130 HCF and LCM of 20 and 65 HCF and LCM of 171 and 209
✅ Answer key — HCF and LCM
HCF = 8, LCM = 832 HCF = 9, LCM = 1134 HCF = 20, LCM = 300 HCF = 7, LCM = 196 HCF = 9, LCM = 990 HCF = 13, LCM = 390 HCF = 5, LCM = 260 HCF = 19, LCM = 1881 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 37
Name: Date: Score: / 8
Find the HCF.
HCF of 500 and 240 (Euclid’s division algorithm) HCF of 301 and 189 (Euclid’s division algorithm) HCF of 825 and 210 (Euclid’s division algorithm) HCF of 322 and 115 (Euclid’s division algorithm) HCF of 324 and 288 (Euclid’s division algorithm) HCF of 588 and 231 (Euclid’s division algorithm) HCF of 703 and 228 (Euclid’s division algorithm) HCF of 656 and 160 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
20 7 15 23 36 21 19 16 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 37
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 440. One number is 55. Find the other. HCF of two numbers is 2 and their LCM is 140. One number is 14. Find the other. HCF of two numbers is 7 and their LCM is 616. One number is 56. Find the other. HCF of two numbers is 5 and their LCM is 180. One number is 45. Find the other. HCF of two numbers is 8 and their LCM is 176. One number is 88. Find the other. HCF of two numbers is 4 and their LCM is 112. One number is 16. Find the other.
✅ Answer key — HCF × LCM = product
88 20 77 20 16 28 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 37
Name: Date: Score: / 8
Answer without long division.
Does 3147/1250 have a terminating decimal expansion? Does 69/25 have a terminating decimal expansion? Does 263/140 have a terminating decimal expansion? Does 2573/880 have a terminating decimal expansion? Does 51/25 have a terminating decimal expansion? Does 1/5 have a terminating decimal expansion? Does 213/125 have a terminating decimal expansion? Does 19/20 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5²) Yes — terminating (denominator 5) Yes — terminating (denominator 5³) Yes — terminating (denominator 2² × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 37
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 6√18 Rational or irrational: 7 + √99 Rational or irrational: 2 + √31 Rational or irrational: √26 Rational or irrational: √74 Rational or irrational: 2√95 Rational or irrational: 7√65 Rational or irrational: √45 Rational or irrational: 4√53 Rational or irrational: 6 + √94 Rational or irrational: 2 + √71 Rational or irrational: 2 + √30
✅ 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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