Free · Class 10 · 6 worksheets · answer keys · practise online · set 5
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 5
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1088 Prime factorisation of 2552 Prime factorisation of 2086 Prime factorisation of 2415 Prime factorisation of 1644 Prime factorisation of 357 Prime factorisation of 2268 Prime factorisation of 2356 Prime factorisation of 992 Prime factorisation of 712
✅ Answer key — Prime factorisation
2⁶ × 17 2³ × 11 × 29 2 × 7 × 149 3 × 5 × 7 × 23 2² × 3 × 137 3 × 7 × 17 2² × 3⁴ × 7 2² × 19 × 31 2⁵ × 31 2³ × 89 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 5
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 100 and 130 HCF and LCM of 209 and 247 HCF and LCM of 40 and 60 HCF and LCM of 133 and 247 HCF and LCM of 65 and 75 HCF and LCM of 18 and 30 HCF and LCM of 110 and 130 HCF and LCM of 63 and 135
✅ Answer key — HCF and LCM
HCF = 10, LCM = 1300 HCF = 19, LCM = 2717 HCF = 20, LCM = 120 HCF = 19, LCM = 1729 HCF = 5, LCM = 975 HCF = 6, LCM = 90 HCF = 10, LCM = 1430 HCF = 9, LCM = 945 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 5
Name: Date: Score: / 8
Find the HCF.
HCF of 215 and 110 (Euclid’s division algorithm) HCF of 600 and 135 (Euclid’s division algorithm) HCF of 840 and 644 (Euclid’s division algorithm) HCF of 891 and 756 (Euclid’s division algorithm) HCF of 893 and 323 (Euclid’s division algorithm) HCF of 295 and 160 (Euclid’s division algorithm) HCF of 114 and 112 (Euclid’s division algorithm) HCF of 174 and 135 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
5 15 28 27 19 5 2 3 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 5
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 567. One number is 63. Find the other. HCF of two numbers is 8 and their LCM is 352. One number is 88. Find the other. HCF of two numbers is 15 and their LCM is 900. One number is 180. Find the other. HCF of two numbers is 12 and their LCM is 264. One number is 132. Find the other. HCF of two numbers is 4 and their LCM is 176. One number is 16. Find the other. HCF of two numbers is 10 and their LCM is 100. One number is 50. Find the other.
✅ Answer key — HCF × LCM = product
81 32 75 24 44 20 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 5
Name: Date: Score: / 8
Answer without long division.
Does 382/625 have a terminating decimal expansion? Does 177/80 have a terminating decimal expansion? Does 3/16 have a terminating decimal expansion? Does 3/5 have a terminating decimal expansion? Does 131/44 have a terminating decimal expansion? Does 7/5 have a terminating decimal expansion? Does 371/1100 have a terminating decimal expansion? Does 64/35 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 5
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√5 Rational or irrational: 8√47 Rational or irrational: 1√89 Rational or irrational: 3√100 Rational or irrational: 5√60 Rational or irrational: 1 + √70 Rational or irrational: 5√25 Rational or irrational: 1 + √23 Rational or irrational: 7√2 Rational or irrational: 2√22 Rational or irrational: 2√88 Rational or irrational: √38
✅ Answer key — Rational or irrational?
irrational irrational irrational rational irrational irrational rational 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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