Free · Class 10 · 6 worksheets · answer keys · practise online · set 66
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 66
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2541 Prime factorisation of 2107 Prime factorisation of 2356 Prime factorisation of 1936 Prime factorisation of 1083 Prime factorisation of 2524 Prime factorisation of 2448 Prime factorisation of 2808 Prime factorisation of 2530 Prime factorisation of 2596
✅ Answer key — Prime factorisation
3 × 7 × 11² 7² × 43 2² × 19 × 31 2⁴ × 11² 3 × 19² 2² × 631 2⁴ × 3² × 17 2³ × 3³ × 13 2 × 5 × 11 × 23 2² × 11 × 59 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 66
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 21 and 28 HCF and LCM of 25 and 55 HCF and LCM of 112 and 182 HCF and LCM of 108 and 132 HCF and LCM of 98 and 112 HCF and LCM of 12 and 52 HCF and LCM of 28 and 98 HCF and LCM of 22 and 26
✅ Answer key — HCF and LCM
HCF = 7, LCM = 84 HCF = 5, LCM = 275 HCF = 14, LCM = 1456 HCF = 12, LCM = 1188 HCF = 14, LCM = 784 HCF = 4, LCM = 156 HCF = 14, LCM = 196 HCF = 2, LCM = 286 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 66
Name: Date: Score: / 8
Find the HCF.
HCF of 315 and 140 (Euclid’s division algorithm) HCF of 468 and 297 (Euclid’s division algorithm) HCF of 946 and 506 (Euclid’s division algorithm) HCF of 987 and 441 (Euclid’s division algorithm) HCF of 875 and 315 (Euclid’s division algorithm) HCF of 264 and 192 (Euclid’s division algorithm) HCF of 377 and 338 (Euclid’s division algorithm) HCF of 774 and 666 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
35 9 22 21 35 24 13 18 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 66
Name: Date: Score: / 6
Solve.
HCF of two numbers is 14 and their LCM is 168. One number is 56. Find the other. HCF of two numbers is 3 and their LCM is 60. One number is 12. Find the other. HCF of two numbers is 14 and their LCM is 1232. One number is 112. Find the other. HCF of two numbers is 4 and their LCM is 112. One number is 28. Find the other. HCF of two numbers is 8 and their LCM is 560. One number is 80. Find the other. HCF of two numbers is 6 and their LCM is 420. One number is 60. Find the other.
✅ Answer key — HCF × LCM = product
42 15 154 16 56 42 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 66
Name: Date: Score: / 8
Answer without long division.
Does 1141/2000 have a terminating decimal expansion? Does 257/100 have a terminating decimal expansion? Does 107/50 have a terminating decimal expansion? Does 43/500 have a terminating decimal expansion? Does 101/40 have a terminating decimal expansion? Does 17/80 have a terminating decimal expansion? Does 211/100 have a terminating decimal expansion? Does 2853/1000 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2⁴ × 5³) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 2³ × 5) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2² × 5²) Yes — terminating (denominator 2³ × 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 66
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √12 Rational or irrational: 3√58 Rational or irrational: 1 + √16 Rational or irrational: √89 Rational or irrational: 4 + √62 Rational or irrational: 3√82 Rational or irrational: 9√42 Rational or irrational: 6 + √77 Rational or irrational: √3 Rational or irrational: 1√51 Rational or irrational: √8 Rational or irrational: 6√22
✅ 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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