Free · Class 10 · 6 worksheets · answer keys · practise online · set 33
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 33
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1100 Prime factorisation of 1950 Prime factorisation of 1323 Prime factorisation of 2055 Prime factorisation of 2430 Prime factorisation of 782 Prime factorisation of 906 Prime factorisation of 930 Prime factorisation of 602 Prime factorisation of 1443
✅ Answer key — Prime factorisation
2² × 5² × 11 2 × 3 × 5² × 13 3³ × 7² 3 × 5 × 137 2 × 3⁵ × 5 2 × 17 × 23 2 × 3 × 151 2 × 3 × 5 × 31 2 × 7 × 43 3 × 13 × 37 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 33
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 36 and 66 HCF and LCM of 35 and 56 HCF and LCM of 198 and 234 HCF and LCM of 42 and 49 HCF and LCM of 25 and 35 HCF and LCM of 64 and 72 HCF and LCM of 64 and 144 HCF and LCM of 154 and 168
✅ Answer key — HCF and LCM
HCF = 6, LCM = 396 HCF = 7, LCM = 280 HCF = 18, LCM = 2574 HCF = 7, LCM = 294 HCF = 5, LCM = 175 HCF = 8, LCM = 576 HCF = 16, LCM = 576 HCF = 14, LCM = 1848 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 33
Name: Date: Score: / 8
Find the HCF.
HCF of 728 and 481 (Euclid’s division algorithm) HCF of 975 and 234 (Euclid’s division algorithm) HCF of 615 and 225 (Euclid’s division algorithm) HCF of 720 and 312 (Euclid’s division algorithm) HCF of 658 and 126 (Euclid’s division algorithm) HCF of 925 and 775 (Euclid’s division algorithm) HCF of 690 and 645 (Euclid’s division algorithm) HCF of 740 and 620 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 39 15 24 14 25 15 20 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 33
Name: Date: Score: / 6
Solve.
HCF of two numbers is 15 and their LCM is 210. One number is 105. Find the other. HCF of two numbers is 6 and their LCM is 462. One number is 42. Find the other. HCF of two numbers is 14 and their LCM is 1008. One number is 126. Find the other. HCF of two numbers is 6 and their LCM is 198. One number is 18. Find the other. HCF of two numbers is 11 and their LCM is 198. One number is 99. Find the other. HCF of two numbers is 4 and their LCM is 528. One number is 48. Find the other.
✅ Answer key — HCF × LCM = product
30 66 112 66 22 44 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 33
Name: Date: Score: / 8
Answer without long division.
Does 119/44 have a terminating decimal expansion? Does 41/125 have a terminating decimal expansion? Does 1/28 have a terminating decimal expansion? Does 41/15 have a terminating decimal expansion? Does 57/20 have a terminating decimal expansion? Does 213/400 have a terminating decimal expansion? Does 1/48 have a terminating decimal expansion? Does 757/880 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 2⁴ × 5²) No — non-terminating repeating (denominator has the factor 3) 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 33
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 7√55 Rational or irrational: √83 Rational or irrational: √12 Rational or irrational: √45 Rational or irrational: √70 Rational or irrational: 6 + √11 Rational or irrational: 7√79 Rational or irrational: 7√50 Rational or irrational: 3 + √12 Rational or irrational: 1√29 Rational or irrational: 2 + √96 Rational or irrational: 6√15
✅ 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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