Free · Class 10 · 6 worksheets · answer keys · practise online · set 91
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 91
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2092 Prime factorisation of 266 Prime factorisation of 504 Prime factorisation of 927 Prime factorisation of 2120 Prime factorisation of 2262 Prime factorisation of 530 Prime factorisation of 2421 Prime factorisation of 2727 Prime factorisation of 130
✅ Answer key — Prime factorisation
2² × 523 2 × 7 × 19 2³ × 3² × 7 3² × 103 2³ × 5 × 53 2 × 3 × 13 × 29 2 × 5 × 53 3² × 269 3³ × 101 2 × 5 × 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 91
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 6 and 26 HCF and LCM of 78 and 169 HCF and LCM of 100 and 140 HCF and LCM of 60 and 220 HCF and LCM of 99 and 108 HCF and LCM of 21 and 35 HCF and LCM of 60 and 200 HCF and LCM of 36 and 90
✅ Answer key — HCF and LCM
HCF = 2, LCM = 78 HCF = 13, LCM = 1014 HCF = 20, LCM = 700 HCF = 20, LCM = 660 HCF = 9, LCM = 1188 HCF = 7, LCM = 105 HCF = 20, LCM = 600 HCF = 18, LCM = 180 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 91
Name: Date: Score: / 8
Find the HCF.
HCF of 184 and 144 (Euclid’s division algorithm) HCF of 561 and 473 (Euclid’s division algorithm) HCF of 222 and 174 (Euclid’s division algorithm) HCF of 285 and 245 (Euclid’s division algorithm) HCF of 750 and 345 (Euclid’s division algorithm) HCF of 688 and 496 (Euclid’s division algorithm) HCF of 720 and 340 (Euclid’s division algorithm) HCF of 240 and 234 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
8 11 6 5 15 16 20 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 91
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 320. One number is 64. Find the other. HCF of two numbers is 12 and their LCM is 1056. One number is 96. Find the other. HCF of two numbers is 9 and their LCM is 252. One number is 36. Find the other. HCF of two numbers is 12 and their LCM is 1320. One number is 120. Find the other. HCF of two numbers is 10 and their LCM is 880. One number is 110. Find the other. HCF of two numbers is 9 and their LCM is 1188. One number is 108. Find the other.
✅ Answer key — HCF × LCM = product
40 132 63 132 80 99 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 91
Name: Date: Score: / 8
Answer without long division.
Does 66/35 have a terminating decimal expansion? Does 5243/2000 have a terminating decimal expansion? Does 35/44 have a terminating decimal expansion? Does 1067/1250 have a terminating decimal expansion? Does 777/325 have a terminating decimal expansion? Does 2209/1040 have a terminating decimal expansion? Does 6/125 have a terminating decimal expansion? Does 409/1400 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2⁴ × 5³) No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2 × 5⁴) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 7) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 91
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 2 + √93 Rational or irrational: 1√16 Rational or irrational: 3 + √3 Rational or irrational: √35 Rational or irrational: 8√94 Rational or irrational: 9√78 Rational or irrational: 3√31 Rational or irrational: √32 Rational or irrational: √41 Rational or irrational: 1 + √74 Rational or irrational: 9 + √14 Rational or irrational: 7 + √84
✅ Answer key — Rational or irrational?
irrational rational 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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