Free · Class 10 · 6 worksheets · answer keys · practise online · set 90
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 90
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2014 Prime factorisation of 1468 Prime factorisation of 910 Prime factorisation of 1750 Prime factorisation of 1776 Prime factorisation of 2100 Prime factorisation of 2834 Prime factorisation of 1864 Prime factorisation of 2580 Prime factorisation of 726
✅ Answer key — Prime factorisation
2 × 19 × 53 2² × 367 2 × 5 × 7 × 13 2 × 5³ × 7 2⁴ × 3 × 37 2² × 3 × 5² × 7 2 × 13 × 109 2³ × 233 2² × 3 × 5 × 43 2 × 3 × 11² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 90
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 36 and 63 HCF and LCM of 45 and 120 HCF and LCM of 28 and 60 HCF and LCM of 52 and 91 HCF and LCM of 39 and 45 HCF and LCM of 220 and 240 HCF and LCM of 66 and 121 HCF and LCM of 12 and 40
✅ Answer key — HCF and LCM
HCF = 9, LCM = 252 HCF = 15, LCM = 360 HCF = 4, LCM = 420 HCF = 13, LCM = 364 HCF = 3, LCM = 585 HCF = 20, LCM = 2640 HCF = 11, LCM = 726 HCF = 4, LCM = 120 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 90
Name: Date: Score: / 8
Find the HCF.
HCF of 836 and 570 (Euclid’s division algorithm) HCF of 684 and 361 (Euclid’s division algorithm) HCF of 154 and 119 (Euclid’s division algorithm) HCF of 212 and 100 (Euclid’s division algorithm) HCF of 344 and 200 (Euclid’s division algorithm) HCF of 893 and 665 (Euclid’s division algorithm) HCF of 172 and 124 (Euclid’s division algorithm) HCF of 396 and 324 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
38 19 7 4 8 19 4 36 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 90
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 132. One number is 33. Find the other. HCF of two numbers is 3 and their LCM is 180. One number is 15. Find the other. HCF of two numbers is 15 and their LCM is 1485. One number is 165. Find the other. HCF of two numbers is 14 and their LCM is 210. One number is 70. Find the other. HCF of two numbers is 2 and their LCM is 36. One number is 18. Find the other. HCF of two numbers is 5 and their LCM is 315. One number is 35. Find the other.
✅ Answer key — HCF × LCM = product
44 36 135 42 4 45 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 90
Name: Date: Score: / 8
Answer without long division.
Does 3/2 have a terminating decimal expansion? Does 127/375 have a terminating decimal expansion? Does 709/625 have a terminating decimal expansion? Does 334/125 have a terminating decimal expansion? Does 1/6 have a terminating decimal expansion? Does 3643/1250 have a terminating decimal expansion? Does 2703/1250 have a terminating decimal expansion? Does 79/176 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2 × 5⁴) 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 90
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 7√68 Rational or irrational: 9 + √50 Rational or irrational: 1 + √81 Rational or irrational: √10 Rational or irrational: 8 + √92 Rational or irrational: √29 Rational or irrational: 7 + √76 Rational or irrational: 5 + √7 Rational or irrational: √79 Rational or irrational: 3 + √94 Rational or irrational: √32 Rational or irrational: √83
✅ Answer key — Rational or irrational?
irrational irrational rational 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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