Free · Class 10 · 6 worksheets · answer keys · practise online · set 45
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 45
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 825 Prime factorisation of 1896 Prime factorisation of 322 Prime factorisation of 2168 Prime factorisation of 615 Prime factorisation of 820 Prime factorisation of 2430 Prime factorisation of 513 Prime factorisation of 578 Prime factorisation of 1250
✅ Answer key — Prime factorisation
3 × 5² × 11 2³ × 3 × 79 2 × 7 × 23 2³ × 271 3 × 5 × 41 2² × 5 × 41 2 × 3⁵ × 5 3³ × 19 2 × 17² 2 × 5⁴ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 45
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 85 and 119 HCF and LCM of 140 and 150 HCF and LCM of 77 and 143 HCF and LCM of 20 and 55 HCF and LCM of 187 and 204 HCF and LCM of 40 and 260 HCF and LCM of 187 and 255 HCF and LCM of 80 and 96
✅ Answer key — HCF and LCM
HCF = 17, LCM = 595 HCF = 10, LCM = 2100 HCF = 11, LCM = 1001 HCF = 5, LCM = 220 HCF = 17, LCM = 2244 HCF = 20, LCM = 520 HCF = 17, LCM = 2805 HCF = 16, LCM = 480 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 45
Name: Date: Score: / 8
Find the HCF.
HCF of 726 and 418 (Euclid’s division algorithm) HCF of 220 and 160 (Euclid’s division algorithm) HCF of 506 and 483 (Euclid’s division algorithm) HCF of 754 and 650 (Euclid’s division algorithm) HCF of 396 and 243 (Euclid’s division algorithm) HCF of 258 and 186 (Euclid’s division algorithm) HCF of 812 and 770 (Euclid’s division algorithm) HCF of 250 and 245 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
22 20 23 26 9 6 14 5 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 45
Name: Date: Score: / 6
Solve.
HCF of two numbers is 12 and their LCM is 540. One number is 60. 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 11 and their LCM is 924. One number is 77. Find the other. HCF of two numbers is 4 and their LCM is 160. One number is 20. Find the other. HCF of two numbers is 15 and their LCM is 1650. One number is 150. Find the other. HCF of two numbers is 9 and their LCM is 891. One number is 99. Find the other.
✅ Answer key — HCF × LCM = product
108 63 132 32 165 81 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 45
Name: Date: Score: / 8
Answer without long division.
Does 841/1300 have a terminating decimal expansion? Does 79/52 have a terminating decimal expansion? Does 135/52 have a terminating decimal expansion? Does 122/125 have a terminating decimal expansion? Does 17/10 have a terminating decimal expansion? Does 111/56 have a terminating decimal expansion? Does 111/55 have a terminating decimal expansion? Does 6/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5³) Yes — terminating (denominator 2 × 5) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 45
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 8√56 Rational or irrational: √39 Rational or irrational: 5 + √17 Rational or irrational: 6√69 Rational or irrational: 7 + √55 Rational or irrational: √40 Rational or irrational: 9√35 Rational or irrational: √48 Rational or irrational: √14 Rational or irrational: 2√87 Rational or irrational: 4 + √76 Rational or irrational: √67
✅ Answer key — Rational or irrational?
irrational 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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