Free · Class 10 · 6 worksheets · answer keys · practise online · set 13
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 13
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1088 Prime factorisation of 1309 Prime factorisation of 175 Prime factorisation of 826 Prime factorisation of 2936 Prime factorisation of 484 Prime factorisation of 144 Prime factorisation of 2288 Prime factorisation of 2626 Prime factorisation of 1809
✅ Answer key — Prime factorisation
2⁶ × 17 7 × 11 × 17 5² × 7 2 × 7 × 59 2³ × 367 2² × 11² 2⁴ × 3² 2⁴ × 11 × 13 2 × 13 × 101 3³ × 67 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 13
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 32 and 240 HCF and LCM of 54 and 78 HCF and LCM of 152 and 247 HCF and LCM of 36 and 52 HCF and LCM of 56 and 63 HCF and LCM of 22 and 55 HCF and LCM of 14 and 91 HCF and LCM of 42 and 91
✅ Answer key — HCF and LCM
HCF = 16, LCM = 480 HCF = 6, LCM = 702 HCF = 19, LCM = 1976 HCF = 4, LCM = 468 HCF = 7, LCM = 504 HCF = 11, LCM = 110 HCF = 7, LCM = 182 HCF = 7, LCM = 546 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 13
Name: Date: Score: / 8
Find the HCF.
HCF of 493 and 290 (Euclid’s division algorithm) HCF of 440 and 154 (Euclid’s division algorithm) HCF of 464 and 377 (Euclid’s division algorithm) HCF of 759 and 713 (Euclid’s division algorithm) HCF of 756 and 742 (Euclid’s division algorithm) HCF of 588 and 308 (Euclid’s division algorithm) HCF of 770 and 574 (Euclid’s division algorithm) HCF of 660 and 200 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
29 22 29 23 14 28 14 20 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 13
Name: Date: Score: / 6
Solve.
HCF of two numbers is 15 and their LCM is 1350. One number is 135. Find the other. HCF of two numbers is 7 and their LCM is 588. One number is 84. Find the other. HCF of two numbers is 9 and their LCM is 216. One number is 27. Find the other. HCF of two numbers is 8 and their LCM is 440. One number is 88. Find the other. HCF of two numbers is 4 and their LCM is 120. One number is 24. Find the other. HCF of two numbers is 2 and their LCM is 120. One number is 24. Find the other.
✅ Answer key — HCF × LCM = product
150 49 72 40 20 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 13
Name: Date: Score: / 8
Answer without long division.
Does 419/350 have a terminating decimal expansion? Does 89/55 have a terminating decimal expansion? Does 1761/1250 have a terminating decimal expansion? Does 68/25 have a terminating decimal expansion? Does 543/220 have a terminating decimal expansion? Does 218/125 have a terminating decimal expansion? Does 31/12 have a terminating decimal expansion? Does 139/52 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 5²) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 3) 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 13
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √36 Rational or irrational: 1√40 Rational or irrational: 3√69 Rational or irrational: √43 Rational or irrational: 8√79 Rational or irrational: 5 + √36 Rational or irrational: √24 Rational or irrational: √92 Rational or irrational: 7√63 Rational or irrational: √47 Rational or irrational: 4√81 Rational or irrational: 1√30
✅ Answer key — Rational or irrational?
rational irrational irrational irrational irrational rational irrational irrational irrational irrational rational 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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