Free · Class 10 · 6 worksheets · answer keys · practise online · set 92
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 92
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 368 Prime factorisation of 384 Prime factorisation of 2732 Prime factorisation of 2698 Prime factorisation of 1260 Prime factorisation of 2428 Prime factorisation of 1353 Prime factorisation of 2692 Prime factorisation of 1644 Prime factorisation of 2238
✅ Answer key — Prime factorisation
2⁴ × 23 2⁷ × 3 2² × 683 2 × 19 × 71 2² × 3² × 5 × 7 2² × 607 3 × 11 × 41 2² × 673 2² × 3 × 137 2 × 3 × 373 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 92
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 48 and 180 HCF and LCM of 132 and 180 HCF and LCM of 24 and 39 HCF and LCM of 21 and 98 HCF and LCM of 39 and 45 HCF and LCM of 40 and 130 HCF and LCM of 221 and 255 HCF and LCM of 75 and 195
✅ Answer key — HCF and LCM
HCF = 12, LCM = 720 HCF = 12, LCM = 1980 HCF = 3, LCM = 312 HCF = 7, LCM = 294 HCF = 3, LCM = 585 HCF = 10, LCM = 520 HCF = 17, LCM = 3315 HCF = 15, LCM = 975 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 92
Name: Date: Score: / 8
Find the HCF.
HCF of 848 and 320 (Euclid’s division algorithm) HCF of 867 and 646 (Euclid’s division algorithm) HCF of 736 and 272 (Euclid’s division algorithm) HCF of 551 and 377 (Euclid’s division algorithm) HCF of 630 and 224 (Euclid’s division algorithm) HCF of 616 and 574 (Euclid’s division algorithm) HCF of 810 and 300 (Euclid’s division algorithm) HCF of 462 and 187 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
16 17 16 29 14 14 30 11 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 92
Name: Date: Score: / 6
Solve.
HCF of two numbers is 9 and their LCM is 567. One number is 81. Find the other. HCF of two numbers is 10 and their LCM is 440. One number is 40. Find the other. HCF of two numbers is 11 and their LCM is 1210. One number is 110. Find the other. HCF of two numbers is 13 and their LCM is 260. One number is 52. Find the other. HCF of two numbers is 5 and their LCM is 110. One number is 10. Find the other. HCF of two numbers is 9 and their LCM is 810. One number is 90. Find the other.
✅ Answer key — HCF × LCM = product
63 110 121 65 55 81 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 92
Name: Date: Score: / 8
Answer without long division.
Does 73/25 have a terminating decimal expansion? Does 323/250 have a terminating decimal expansion? Does 5/2 have a terminating decimal expansion? Does 4182/1625 have a terminating decimal expansion? Does 36/175 have a terminating decimal expansion? Does 37/500 have a terminating decimal expansion? Does 107/100 have a terminating decimal expansion? Does 251/1375 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 5²) Yes — terminating (denominator 2 × 5³) Yes — terminating (denominator 2) No — non-terminating repeating (denominator has the factor 13) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2² × 5³) Yes — terminating (denominator 2² × 5²) 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 92
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √50 Rational or irrational: √67 Rational or irrational: 3√28 Rational or irrational: √49 Rational or irrational: 3√23 Rational or irrational: 4 + √3 Rational or irrational: 8√69 Rational or irrational: 6√24 Rational or irrational: √94 Rational or irrational: 4√92 Rational or irrational: √15 Rational or irrational: 3 + √41
✅ Answer key — Rational or irrational?
irrational irrational irrational rational 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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