Free · Class 10 · 6 worksheets · answer keys · practise online · set 79
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 79
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2282 Prime factorisation of 1001 Prime factorisation of 1995 Prime factorisation of 426 Prime factorisation of 1372 Prime factorisation of 2070 Prime factorisation of 855 Prime factorisation of 948 Prime factorisation of 2216 Prime factorisation of 1311
✅ Answer key — Prime factorisation
2 × 7 × 163 7 × 11 × 13 3 × 5 × 7 × 19 2 × 3 × 71 2² × 7³ 2 × 3² × 5 × 23 3² × 5 × 19 2² × 3 × 79 2³ × 277 3 × 19 × 23 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 79
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 56 and 80 HCF and LCM of 49 and 105 HCF and LCM of 180 and 198 HCF and LCM of 88 and 104 HCF and LCM of 154 and 165 HCF and LCM of 44 and 143 HCF and LCM of 40 and 260 HCF and LCM of 4 and 6
✅ Answer key — HCF and LCM
HCF = 8, LCM = 560 HCF = 7, LCM = 735 HCF = 18, LCM = 1980 HCF = 8, LCM = 1144 HCF = 11, LCM = 2310 HCF = 11, LCM = 572 HCF = 20, LCM = 520 HCF = 2, LCM = 12 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 79
Name: Date: Score: / 8
Find the HCF.
HCF of 722 and 342 (Euclid’s division algorithm) HCF of 644 and 437 (Euclid’s division algorithm) HCF of 228 and 156 (Euclid’s division algorithm) HCF of 420 and 340 (Euclid’s division algorithm) HCF of 851 and 713 (Euclid’s division algorithm) HCF of 232 and 192 (Euclid’s division algorithm) HCF of 399 and 361 (Euclid’s division algorithm) HCF of 282 and 120 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
38 23 12 20 23 8 19 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 79
Name: Date: Score: / 6
Solve.
HCF of two numbers is 2 and their LCM is 176. One number is 16. Find the other. HCF of two numbers is 9 and their LCM is 540. One number is 108. Find the other. HCF of two numbers is 9 and their LCM is 90. One number is 18. Find the other. HCF of two numbers is 8 and their LCM is 480. One number is 96. Find the other. HCF of two numbers is 7 and their LCM is 252. One number is 63. Find the other. HCF of two numbers is 15 and their LCM is 1320. One number is 120. Find the other.
✅ Answer key — HCF × LCM = product
22 45 45 40 28 165 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 79
Name: Date: Score: / 8
Answer without long division.
Does 89/550 have a terminating decimal expansion? Does 1/8 have a terminating decimal expansion? Does 47/22 have a terminating decimal expansion? Does 1393/500 have a terminating decimal expansion? Does 1/5 have a terminating decimal expansion? Does 9/4 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 4859/1875 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 5) Yes — terminating (denominator 2²) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 3) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 79
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √46 Rational or irrational: √65 Rational or irrational: 9√86 Rational or irrational: 2 + √62 Rational or irrational: √60 Rational or irrational: √91 Rational or irrational: 2 + √36 Rational or irrational: √68 Rational or irrational: 6 + √90 Rational or irrational: 7√70 Rational or irrational: √50 Rational or irrational: √100
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational rational irrational irrational irrational irrational rational 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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