Free · Class 10 · 6 worksheets · answer keys · practise online · set 26
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 26
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 956 Prime factorisation of 2016 Prime factorisation of 2212 Prime factorisation of 2796 Prime factorisation of 1722 Prime factorisation of 2871 Prime factorisation of 682 Prime factorisation of 2665 Prime factorisation of 2184 Prime factorisation of 306
✅ Answer key — Prime factorisation
2² × 239 2⁵ × 3² × 7 2² × 7 × 79 2² × 3 × 233 2 × 3 × 7 × 41 3² × 11 × 29 2 × 11 × 31 5 × 13 × 41 2³ × 3 × 7 × 13 2 × 3² × 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 26
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 84 and 91 HCF and LCM of 20 and 50 HCF and LCM of 24 and 42 HCF and LCM of 15 and 24 HCF and LCM of 108 and 234 HCF and LCM of 54 and 90 HCF and LCM of 10 and 25 HCF and LCM of 81 and 126
✅ Answer key — HCF and LCM
HCF = 7, LCM = 1092 HCF = 10, LCM = 100 HCF = 6, LCM = 168 HCF = 3, LCM = 120 HCF = 18, LCM = 1404 HCF = 18, LCM = 270 HCF = 5, LCM = 50 HCF = 9, LCM = 1134 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 26
Name: Date: Score: / 8
Find the HCF.
HCF of 352 and 216 (Euclid’s division algorithm) HCF of 399 and 361 (Euclid’s division algorithm) HCF of 608 and 418 (Euclid’s division algorithm) HCF of 410 and 100 (Euclid’s division algorithm) HCF of 589 and 399 (Euclid’s division algorithm) HCF of 118 and 102 (Euclid’s division algorithm) HCF of 522 and 117 (Euclid’s division algorithm) HCF of 377 and 203 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
8 19 38 10 19 2 9 29 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 26
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 28. One number is 14. Find the other. HCF of two numbers is 2 and their LCM is 144. One number is 16. Find the other. HCF of two numbers is 10 and their LCM is 560. One number is 70. Find the other. HCF of two numbers is 9 and their LCM is 405. One number is 45. Find the other. HCF of two numbers is 7 and their LCM is 168. One number is 21. Find the other. HCF of two numbers is 7 and their LCM is 84. One number is 21. Find the other.
✅ Answer key — HCF × LCM = product
4 18 80 81 56 28 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 26
Name: Date: Score: / 8
Answer without long division.
Does 377/625 have a terminating decimal expansion? Does 397/220 have a terminating decimal expansion? Does 14/5 have a terminating decimal expansion? Does 491/280 have a terminating decimal expansion? Does 857/550 have a terminating decimal expansion? Does 6/25 have a terminating decimal expansion? Does 2619/1625 have a terminating decimal expansion? Does 881/880 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 13) 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 26
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √16 Rational or irrational: 9√34 Rational or irrational: √90 Rational or irrational: √46 Rational or irrational: 5√56 Rational or irrational: √41 Rational or irrational: 8√88 Rational or irrational: √37 Rational or irrational: 4 + √59 Rational or irrational: 6 + √67 Rational or irrational: √10 Rational or irrational: √7
✅ Answer key — Rational or irrational?
rational 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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