Free · Class 10 · 6 worksheets · answer keys · practise online · set 9
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 9
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 722 Prime factorisation of 846 Prime factorisation of 1600 Prime factorisation of 644 Prime factorisation of 345 Prime factorisation of 1802 Prime factorisation of 2685 Prime factorisation of 950 Prime factorisation of 128 Prime factorisation of 363
✅ Answer key — Prime factorisation
2 × 19² 2 × 3² × 47 2⁶ × 5² 2² × 7 × 23 3 × 5 × 23 2 × 17 × 53 3 × 5 × 179 2 × 5² × 19 2⁷ 3 × 11² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 9
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 70 and 98 HCF and LCM of 48 and 160 HCF and LCM of 42 and 78 HCF and LCM of 6 and 39 HCF and LCM of 12 and 44 HCF and LCM of 144 and 208 HCF and LCM of 117 and 169 HCF and LCM of 60 and 78
✅ Answer key — HCF and LCM
HCF = 14, LCM = 490 HCF = 16, LCM = 480 HCF = 6, LCM = 546 HCF = 3, LCM = 78 HCF = 4, LCM = 132 HCF = 16, LCM = 1872 HCF = 13, LCM = 1521 HCF = 6, LCM = 780 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 9
Name: Date: Score: / 8
Find the HCF.
HCF of 777 and 189 (Euclid’s division algorithm) HCF of 725 and 375 (Euclid’s division algorithm) HCF of 290 and 240 (Euclid’s division algorithm) HCF of 456 and 328 (Euclid’s division algorithm) HCF of 704 and 592 (Euclid’s division algorithm) HCF of 640 and 464 (Euclid’s division algorithm) HCF of 888 and 864 (Euclid’s division algorithm) HCF of 546 and 392 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
21 25 10 8 16 16 24 14 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 9
Name: Date: Score: / 6
Solve.
HCF of two numbers is 13 and their LCM is 390. One number is 39. Find the other. HCF of two numbers is 5 and their LCM is 440. One number is 40. Find the other. HCF of two numbers is 7 and their LCM is 315. One number is 35. Find the other. HCF of two numbers is 9 and their LCM is 792. One number is 72. Find the other. HCF of two numbers is 6 and their LCM is 264. One number is 66. Find the other. HCF of two numbers is 12 and their LCM is 288. One number is 36. Find the other.
✅ Answer key — HCF × LCM = product
130 55 63 99 24 96 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 9
Name: Date: Score: / 8
Answer without long division.
Does 353/120 have a terminating decimal expansion? Does 126/125 have a terminating decimal expansion? Does 569/260 have a terminating decimal expansion? Does 9/5 have a terminating decimal expansion? Does 13/16 have a terminating decimal expansion? Does 1096/625 have a terminating decimal expansion? Does 2136/875 have a terminating decimal expansion? Does 13/22 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 7) 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 9
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 2 + √58 Rational or irrational: √79 Rational or irrational: 4√16 Rational or irrational: √22 Rational or irrational: √71 Rational or irrational: 2√71 Rational or irrational: 3 + √78 Rational or irrational: 6√79 Rational or irrational: 3√76 Rational or irrational: 9 + √27 Rational or irrational: 4 + √78 Rational or irrational: 2√37
✅ Answer key — Rational or irrational?
irrational irrational rational 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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