Free · Class 10 · 6 worksheets · answer keys · practise online · set 2
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 2
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 819 Prime factorisation of 668 Prime factorisation of 2224 Prime factorisation of 444 Prime factorisation of 2121 Prime factorisation of 426 Prime factorisation of 1072 Prime factorisation of 2667 Prime factorisation of 2876 Prime factorisation of 1610
✅ Answer key — Prime factorisation
3² × 7 × 13 2² × 167 2⁴ × 139 2² × 3 × 37 3 × 7 × 101 2 × 3 × 71 2⁴ × 67 3 × 7 × 127 2² × 719 2 × 5 × 7 × 23 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 2
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 20 and 52 HCF and LCM of 12 and 40 HCF and LCM of 171 and 190 HCF and LCM of 54 and 198 HCF and LCM of 54 and 60 HCF and LCM of 200 and 220 HCF and LCM of 126 and 270 HCF and LCM of 77 and 121
✅ Answer key — HCF and LCM
HCF = 4, LCM = 260 HCF = 4, LCM = 120 HCF = 19, LCM = 1710 HCF = 18, LCM = 594 HCF = 6, LCM = 540 HCF = 20, LCM = 2200 HCF = 18, LCM = 1890 HCF = 11, LCM = 847 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 2
Name: Date: Score: / 8
Find the HCF.
HCF of 420 and 225 (Euclid’s division algorithm) HCF of 275 and 195 (Euclid’s division algorithm) HCF of 940 and 320 (Euclid’s division algorithm) HCF of 325 and 300 (Euclid’s division algorithm) HCF of 540 and 390 (Euclid’s division algorithm) HCF of 448 and 440 (Euclid’s division algorithm) HCF of 450 and 189 (Euclid’s division algorithm) HCF of 504 and 156 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
15 5 20 25 30 8 9 12 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 2
Name: Date: Score: / 6
Solve.
HCF of two numbers is 6 and their LCM is 360. One number is 30. Find the other. HCF of two numbers is 15 and their LCM is 1050. One number is 150. Find the other. HCF of two numbers is 12 and their LCM is 432. One number is 108. Find the other. HCF of two numbers is 3 and their LCM is 297. One number is 33. Find the other. HCF of two numbers is 6 and their LCM is 528. One number is 66. Find the other. HCF of two numbers is 9 and their LCM is 504. One number is 72. Find the other.
✅ Answer key — HCF × LCM = product
72 105 48 27 48 63 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 2
Name: Date: Score: / 8
Answer without long division.
Does 17/25 have a terminating decimal expansion? Does 1/25 have a terminating decimal expansion? Does 7/16 have a terminating decimal expansion? Does 669/250 have a terminating decimal expansion? Does 52/25 have a terminating decimal expansion? Does 1587/1000 have a terminating decimal expansion? Does 41/15 have a terminating decimal expansion? Does 1779/2000 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) Yes — terminating (denominator 5²) Yes — terminating (denominator 2⁴) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 5²) Yes — terminating (denominator 2³ × 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2⁴ × 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 2
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 3√45 Rational or irrational: 2 + √2 Rational or irrational: 4 + √4 Rational or irrational: 2 + √57 Rational or irrational: 6 + √88 Rational or irrational: √96 Rational or irrational: √18 Rational or irrational: 9√50 Rational or irrational: 2√65 Rational or irrational: 4√51 Rational or irrational: 8 + √22 Rational or irrational: 7√27
✅ 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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