Free · Class 10 · 6 worksheets · answer keys · practise online · set 93
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 93
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 2164 Prime factorisation of 2946 Prime factorisation of 300 Prime factorisation of 2384 Prime factorisation of 160 Prime factorisation of 2848 Prime factorisation of 2967 Prime factorisation of 1166 Prime factorisation of 1278 Prime factorisation of 686
✅ Answer key — Prime factorisation
2² × 541 2 × 3 × 491 2² × 3 × 5² 2⁴ × 149 2⁵ × 5 2⁵ × 89 3 × 23 × 43 2 × 11 × 53 2 × 3² × 71 2 × 7³ TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 93
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 90 and 108 HCF and LCM of 90 and 216 HCF and LCM of 60 and 132 HCF and LCM of 27 and 33 HCF and LCM of 140 and 160 HCF and LCM of 25 and 35 HCF and LCM of 91 and 105 HCF and LCM of 154 and 168
✅ Answer key — HCF and LCM
HCF = 18, LCM = 540 HCF = 18, LCM = 1080 HCF = 12, LCM = 660 HCF = 3, LCM = 297 HCF = 20, LCM = 1120 HCF = 5, LCM = 175 HCF = 7, LCM = 1365 HCF = 14, LCM = 1848 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 93
Name: Date: Score: / 8
Find the HCF.
HCF of 423 and 297 (Euclid’s division algorithm) HCF of 880 and 460 (Euclid’s division algorithm) HCF of 625 and 225 (Euclid’s division algorithm) HCF of 329 and 217 (Euclid’s division algorithm) HCF of 410 and 140 (Euclid’s division algorithm) HCF of 528 and 360 (Euclid’s division algorithm) HCF of 975 and 663 (Euclid’s division algorithm) HCF of 580 and 110 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
9 20 25 7 10 24 39 10 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 93
Name: Date: Score: / 6
Solve.
HCF of two numbers is 5 and their LCM is 280. One number is 35. Find the other. HCF of two numbers is 9 and their LCM is 180. One number is 36. Find the other. HCF of two numbers is 5 and their LCM is 495. One number is 45. Find the other. HCF of two numbers is 8 and their LCM is 720. One number is 80. Find the other. HCF of two numbers is 11 and their LCM is 924. One number is 132. Find the other. HCF of two numbers is 13 and their LCM is 780. One number is 156. Find the other.
✅ Answer key — HCF × LCM = product
40 45 55 72 77 65 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 93
Name: Date: Score: / 8
Answer without long division.
Does 63/25 have a terminating decimal expansion? Does 9/8 have a terminating decimal expansion? Does 407/140 have a terminating decimal expansion? Does 278/125 have a terminating decimal expansion? Does 29/10 have a terminating decimal expansion? Does 119/50 have a terminating decimal expansion? Does 3/2 have a terminating decimal expansion? Does 1653/625 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) Yes — terminating (denominator 2³) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 5³) Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2 × 5²) Yes — terminating (denominator 2) Yes — terminating (denominator 5⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 93
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 9 + √73 Rational or irrational: 5√65 Rational or irrational: 8√5 Rational or irrational: 2√93 Rational or irrational: √83 Rational or irrational: √98 Rational or irrational: 8√54 Rational or irrational: 8√19 Rational or irrational: 7 + √80 Rational or irrational: 5√45 Rational or irrational: 1 + √66 Rational or irrational: 3√26
✅ Answer key — Rational or irrational?
irrational irrational irrational 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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