Free · Class 10 · 6 worksheets · answer keys · practise online · set 64
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 64
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1916 Prime factorisation of 2864 Prime factorisation of 1696 Prime factorisation of 1988 Prime factorisation of 980 Prime factorisation of 2750 Prime factorisation of 744 Prime factorisation of 2958 Prime factorisation of 1464 Prime factorisation of 741
✅ Answer key — Prime factorisation
2² × 479 2⁴ × 179 2⁵ × 53 2² × 7 × 71 2² × 5 × 7² 2 × 5³ × 11 2³ × 3 × 31 2 × 3 × 17 × 29 2³ × 3 × 61 3 × 13 × 19 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 64
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 34 and 153 HCF and LCM of 84 and 182 HCF and LCM of 70 and 75 HCF and LCM of 108 and 198 HCF and LCM of 70 and 182 HCF and LCM of 9 and 24 HCF and LCM of 28 and 182 HCF and LCM of 117 and 135
✅ Answer key — HCF and LCM
HCF = 17, LCM = 306 HCF = 14, LCM = 1092 HCF = 5, LCM = 1050 HCF = 18, LCM = 1188 HCF = 14, LCM = 910 HCF = 3, LCM = 72 HCF = 14, LCM = 364 HCF = 9, LCM = 1755 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 64
Name: Date: Score: / 8
Find the HCF.
HCF of 864 and 208 (Euclid’s division algorithm) HCF of 224 and 220 (Euclid’s division algorithm) HCF of 861 and 168 (Euclid’s division algorithm) HCF of 740 and 300 (Euclid’s division algorithm) HCF of 620 and 527 (Euclid’s division algorithm) HCF of 413 and 182 (Euclid’s division algorithm) HCF of 841 and 493 (Euclid’s division algorithm) HCF of 544 and 119 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
16 4 21 20 31 7 29 17 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 64
Name: Date: Score: / 6
Solve.
HCF of two numbers is 3 and their LCM is 231. One number is 21. Find the other. HCF of two numbers is 15 and their LCM is 600. One number is 75. Find the other. HCF of two numbers is 6 and their LCM is 132. One number is 66. Find the other. HCF of two numbers is 5 and their LCM is 210. One number is 30. Find the other. HCF of two numbers is 5 and their LCM is 450. One number is 50. Find the other. HCF of two numbers is 13 and their LCM is 1716. One number is 143. Find the other.
✅ Answer key — HCF × LCM = product
33 120 12 35 45 156 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 64
Name: Date: Score: / 8
Answer without long division.
Does 1854/1375 have a terminating decimal expansion? Does 5079/2000 have a terminating decimal expansion? Does 322/325 have a terminating decimal expansion? Does 389/208 have a terminating decimal expansion? Does 73/88 have a terminating decimal expansion? Does 249/140 have a terminating decimal expansion? Does 29/10 have a terminating decimal expansion? Does 71/40 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
No — non-terminating repeating (denominator has the factor 11) Yes — terminating (denominator 2⁴ × 5³) 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 11) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2³ × 5) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 64
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 4√39 Rational or irrational: 9√48 Rational or irrational: 8√51 Rational or irrational: 2 + √72 Rational or irrational: 2√87 Rational or irrational: 7√36 Rational or irrational: √78 Rational or irrational: √74 Rational or irrational: 4√91 Rational or irrational: √25 Rational or irrational: 4 + √91 Rational or irrational: √9
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational rational irrational irrational irrational rational irrational rational 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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