Free · Class 10 · 6 worksheets · answer keys · practise online · set 24
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 24
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 322 Prime factorisation of 2844 Prime factorisation of 1827 Prime factorisation of 2373 Prime factorisation of 2673 Prime factorisation of 528 Prime factorisation of 1912 Prime factorisation of 2562 Prime factorisation of 832 Prime factorisation of 2585
✅ Answer key — Prime factorisation
2 × 7 × 23 2² × 3² × 79 3² × 7 × 29 3 × 7 × 113 3⁵ × 11 2⁴ × 3 × 11 2³ × 239 2 × 3 × 7 × 61 2⁶ × 13 5 × 11 × 47 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 24
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 64 and 144 HCF and LCM of 22 and 33 HCF and LCM of 160 and 300 HCF and LCM of 42 and 45 HCF and LCM of 140 and 182 HCF and LCM of 75 and 180 HCF and LCM of 40 and 104 HCF and LCM of 90 and 198
✅ Answer key — HCF and LCM
HCF = 16, LCM = 576 HCF = 11, LCM = 66 HCF = 20, LCM = 2400 HCF = 3, LCM = 630 HCF = 14, LCM = 1820 HCF = 15, LCM = 900 HCF = 8, LCM = 520 HCF = 18, LCM = 990 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 24
Name: Date: Score: / 8
Find the HCF.
HCF of 864 and 560 (Euclid’s division algorithm) HCF of 273 and 119 (Euclid’s division algorithm) HCF of 658 and 154 (Euclid’s division algorithm) HCF of 370 and 340 (Euclid’s division algorithm) HCF of 608 and 361 (Euclid’s division algorithm) HCF of 756 and 306 (Euclid’s division algorithm) HCF of 782 and 425 (Euclid’s division algorithm) HCF of 351 and 130 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
16 7 14 10 19 18 17 13 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 24
Name: Date: Score: / 6
Solve.
HCF of two numbers is 11 and their LCM is 693. One number is 77. Find the other. HCF of two numbers is 2 and their LCM is 20. One number is 10. Find the other. HCF of two numbers is 7 and their LCM is 539. One number is 77. Find the other. HCF of two numbers is 6 and their LCM is 264. One number is 24. Find the other. HCF of two numbers is 15 and their LCM is 450. One number is 90. Find the other. HCF of two numbers is 13 and their LCM is 780. One number is 65. Find the other.
✅ Answer key — HCF × LCM = product
99 4 49 66 75 156 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 24
Name: Date: Score: / 8
Answer without long division.
Does 7/4 have a terminating decimal expansion? Does 2719/1400 have a terminating decimal expansion? Does 1651/600 have a terminating decimal expansion? Does 1162/625 have a terminating decimal expansion? Does 158/125 have a terminating decimal expansion? Does 25/24 have a terminating decimal expansion? Does 1049/1250 have a terminating decimal expansion? Does 37/16 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 7) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 5⁴) Yes — terminating (denominator 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2 × 5⁴) Yes — terminating (denominator 2⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 24
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 3√52 Rational or irrational: 4√35 Rational or irrational: 7 + √45 Rational or irrational: 4√83 Rational or irrational: √40 Rational or irrational: 6√17 Rational or irrational: √24 Rational or irrational: 6 + √46 Rational or irrational: √18 Rational or irrational: 4 + √70 Rational or irrational: √86 Rational or irrational: 1√78
✅ 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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