Free · Class 10 · 6 worksheets · answer keys · practise online · set 70
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 70
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 822 Prime factorisation of 1444 Prime factorisation of 2340 Prime factorisation of 1495 Prime factorisation of 764 Prime factorisation of 1396 Prime factorisation of 2300 Prime factorisation of 1419 Prime factorisation of 2738 Prime factorisation of 1557
✅ Answer key — Prime factorisation
2 × 3 × 137 2² × 19² 2² × 3² × 5 × 13 5 × 13 × 23 2² × 191 2² × 349 2² × 5² × 23 3 × 11 × 43 2 × 37² 3² × 173 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 70
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 136 and 187 HCF and LCM of 60 and 72 HCF and LCM of 90 and 130 HCF and LCM of 160 and 220 HCF and LCM of 15 and 55 HCF and LCM of 95 and 209 HCF and LCM of 15 and 40 HCF and LCM of 112 and 208
✅ Answer key — HCF and LCM
HCF = 17, LCM = 1496 HCF = 12, LCM = 360 HCF = 10, LCM = 1170 HCF = 20, LCM = 1760 HCF = 5, LCM = 165 HCF = 19, LCM = 1045 HCF = 5, LCM = 120 HCF = 16, LCM = 1456 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 70
Name: Date: Score: / 8
Find the HCF.
HCF of 644 and 616 (Euclid’s division algorithm) HCF of 930 and 150 (Euclid’s division algorithm) HCF of 132 and 105 (Euclid’s division algorithm) HCF of 592 and 272 (Euclid’s division algorithm) HCF of 850 and 459 (Euclid’s division algorithm) HCF of 702 and 286 (Euclid’s division algorithm) HCF of 740 and 420 (Euclid’s division algorithm) HCF of 752 and 528 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
28 30 3 16 17 26 20 16 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 70
Name: Date: Score: / 6
Solve.
HCF of two numbers is 8 and their LCM is 320. One number is 40. Find the other. HCF of two numbers is 14 and their LCM is 252. One number is 28. Find the other. HCF of two numbers is 12 and their LCM is 1080. One number is 120. Find the other. HCF of two numbers is 4 and their LCM is 120. One number is 12. Find the other. HCF of two numbers is 8 and their LCM is 616. One number is 56. Find the other. HCF of two numbers is 2 and their LCM is 176. One number is 16. Find the other.
✅ Answer key — HCF × LCM = product
64 126 108 40 88 22 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 70
Name: Date: Score: / 8
Answer without long division.
Does 27/10 have a terminating decimal expansion? Does 51/20 have a terminating decimal expansion? Does 1/2 have a terminating decimal expansion? Does 51/400 have a terminating decimal expansion? Does 1/4 have a terminating decimal expansion? Does 187/280 have a terminating decimal expansion? Does 13/10 have a terminating decimal expansion? Does 3523/1250 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2² × 5) Yes — terminating (denominator 2) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 2²) No — non-terminating repeating (denominator has the factor 7) Yes — terminating (denominator 2 × 5) Yes — terminating (denominator 2 × 5⁴) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 70
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: 5 + √86 Rational or irrational: 2√96 Rational or irrational: 7√28 Rational or irrational: √60 Rational or irrational: 2√66 Rational or irrational: 7 + √17 Rational or irrational: 6√54 Rational or irrational: √18 Rational or irrational: 1 + √5 Rational or irrational: 7 + √94 Rational or irrational: 3√56 Rational or irrational: √87
✅ 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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