Free · Class 10 · 6 worksheets · answer keys · practise online · set 55
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 55
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2575 Prime factorisation of 2084 Prime factorisation of 1348 Prime factorisation of 2082 Prime factorisation of 1080 Prime factorisation of 2008 Prime factorisation of 2348 Prime factorisation of 2430 Prime factorisation of 725 Prime factorisation of 236
✅ Answer key — Prime factorisation
5² × 103 2² × 521 2² × 337 2 × 3 × 347 2³ × 3³ × 5 2³ × 251 2² × 587 2 × 3⁵ × 5 5² × 29 2² × 59 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 55
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 66 and 78 HCF and LCM of 121 and 132 HCF and LCM of 99 and 110 HCF and LCM of 168 and 180 HCF and LCM of 9 and 24 HCF and LCM of 36 and 56 HCF and LCM of 21 and 36 HCF and LCM of 114 and 209
✅ Answer key — HCF and LCM
HCF = 6, LCM = 858 HCF = 11, LCM = 1452 HCF = 11, LCM = 990 HCF = 12, LCM = 2520 HCF = 3, LCM = 72 HCF = 4, LCM = 504 HCF = 3, LCM = 252 HCF = 19, LCM = 1254 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 55
Name: Date: Score: / 8
Find the HCF.
HCF of 645 and 150 (Euclid’s division algorithm) HCF of 567 and 351 (Euclid’s division algorithm) HCF of 598 and 529 (Euclid’s division algorithm) HCF of 945 and 280 (Euclid’s division algorithm) HCF of 893 and 152 (Euclid’s division algorithm) HCF of 423 and 171 (Euclid’s division algorithm) HCF of 513 and 504 (Euclid’s division algorithm) HCF of 690 and 510 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
15 27 23 35 19 9 9 30 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 55
Name: Date: Score: / 6
Solve.
HCF of two numbers is 7 and their LCM is 588. One number is 84. Find the other. HCF of two numbers is 10 and their LCM is 180. One number is 20. Find the other. HCF of two numbers is 15 and their LCM is 990. One number is 90. Find the other. HCF of two numbers is 14 and their LCM is 1008. One number is 112. Find the other. HCF of two numbers is 12 and their LCM is 864. One number is 96. Find the other. HCF of two numbers is 4 and their LCM is 176. One number is 16. Find the other.
✅ Answer key — HCF × LCM = product
49 90 165 126 108 44 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 55
Name: Date: Score: / 8
Answer without long division.
Does 1002/625 have a terminating decimal expansion? Does 1124/625 have a terminating decimal expansion? Does 49/88 have a terminating decimal expansion? Does 871/350 have a terminating decimal expansion? Does 33/20 have a terminating decimal expansion? Does 1211/650 have a terminating decimal expansion? Does 178/125 have a terminating decimal expansion? Does 6/5 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5⁴) No — non-terminating repeating (denominator has the factor 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5) No — non-terminating repeating (denominator has the factor 13) Yes — terminating (denominator 5³) 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 55
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √98 Rational or irrational: 1 + √74 Rational or irrational: √73 Rational or irrational: 4√43 Rational or irrational: 8 + √8 Rational or irrational: 9√60 Rational or irrational: 7√41 Rational or irrational: 3 + √73 Rational or irrational: 5 + √43 Rational or irrational: 3 + √46 Rational or irrational: 5 + √99 Rational or irrational: √34
✅ 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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