Free · Class 10 · 6 worksheets · answer keys · practise online · set 53
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 53
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1866 Prime factorisation of 686 Prime factorisation of 1640 Prime factorisation of 2006 Prime factorisation of 2970 Prime factorisation of 1040 Prime factorisation of 768 Prime factorisation of 1911 Prime factorisation of 324 Prime factorisation of 726
✅ Answer key — Prime factorisation
2 × 3 × 311 2 × 7³ 2³ × 5 × 41 2 × 17 × 59 2 × 3³ × 5 × 11 2⁴ × 5 × 13 2⁸ × 3 3 × 7² × 13 2² × 3⁴ 2 × 3 × 11² TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 53
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 160 and 300 HCF and LCM of 91 and 143 HCF and LCM of 12 and 26 HCF and LCM of 40 and 56 HCF and LCM of 55 and 154 HCF and LCM of 54 and 60 HCF and LCM of 25 and 70 HCF and LCM of 36 and 81
✅ Answer key — HCF and LCM
HCF = 20, LCM = 2400 HCF = 13, LCM = 1001 HCF = 2, LCM = 156 HCF = 8, LCM = 280 HCF = 11, LCM = 770 HCF = 6, LCM = 540 HCF = 5, LCM = 350 HCF = 9, LCM = 324 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 53
Name: Date: Score: / 8
Find the HCF.
HCF of 455 and 377 (Euclid’s division algorithm) HCF of 400 and 176 (Euclid’s division algorithm) HCF of 936 and 342 (Euclid’s division algorithm) HCF of 352 and 275 (Euclid’s division algorithm) HCF of 884 and 182 (Euclid’s division algorithm) HCF of 425 and 374 (Euclid’s division algorithm) HCF of 481 and 377 (Euclid’s division algorithm) HCF of 530 and 440 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
13 16 18 11 26 17 13 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 53
Name: Date: Score: / 6
Solve.
HCF of two numbers is 5 and their LCM is 360. One number is 40. Find the other. HCF of two numbers is 13 and their LCM is 572. One number is 143. Find the other. HCF of two numbers is 13 and their LCM is 520. One number is 104. Find the other. HCF of two numbers is 8 and their LCM is 504. One number is 56. Find the other. HCF of two numbers is 12 and their LCM is 168. One number is 24. Find the other. HCF of two numbers is 15 and their LCM is 315. One number is 105. Find the other.
✅ Answer key — HCF × LCM = product
45 52 65 72 84 45 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 53
Name: Date: Score: / 8
Answer without long division.
Does 451/500 have a terminating decimal expansion? Does 67/30 have a terminating decimal expansion? Does 67/50 have a terminating decimal expansion? Does 33/200 have a terminating decimal expansion? Does 33/20 have a terminating decimal expansion? Does 307/200 have a terminating decimal expansion? Does 49/120 have a terminating decimal expansion? Does 1073/440 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 2³ × 5²) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 2³ × 5²) No — non-terminating repeating (denominator has the factor 3) 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 53
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 3√63 Rational or irrational: √65 Rational or irrational: 6 + √68 Rational or irrational: √56 Rational or irrational: 6 + √71 Rational or irrational: 3√74 Rational or irrational: 9 + √25 Rational or irrational: √45 Rational or irrational: √61 Rational or irrational: √47 Rational or irrational: √88 Rational or irrational: √30
✅ Answer key — Rational or irrational?
irrational irrational irrational irrational irrational irrational rational 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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