Free · Class 10 · 6 worksheets · answer keys · practise online · set 73
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 73
Name: Date: Score: / 10
Write as a product of primes (use powers).
Prime factorisation of 1617 Prime factorisation of 580 Prime factorisation of 2216 Prime factorisation of 1776 Prime factorisation of 2035 Prime factorisation of 966 Prime factorisation of 850 Prime factorisation of 872 Prime factorisation of 2092 Prime factorisation of 1932
✅ Answer key — Prime factorisation
3 × 7² × 11 2² × 5 × 29 2³ × 277 2⁴ × 3 × 37 5 × 11 × 37 2 × 3 × 7 × 23 2 × 5² × 17 2³ × 109 2² × 523 2² × 3 × 7 × 23 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF and LCM Class 10 · Worksheet 2 · set 73
Name: Date: Score: / 8
Find the HCF and LCM by prime factorisation.
HCF and LCM of 56 and 104 HCF and LCM of 60 and 110 HCF and LCM of 220 and 240 HCF and LCM of 40 and 88 HCF and LCM of 4 and 22 HCF and LCM of 4 and 6 HCF and LCM of 22 and 55 HCF and LCM of 54 and 117
✅ Answer key — HCF and LCM
HCF = 8, LCM = 728 HCF = 10, LCM = 660 HCF = 20, LCM = 2640 HCF = 8, LCM = 440 HCF = 2, LCM = 44 HCF = 2, LCM = 12 HCF = 11, LCM = 110 HCF = 9, LCM = 702 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Euclid’s division algorithm Class 10 · Worksheet 3 · set 73
Name: Date: Score: / 8
Find the HCF.
HCF of 782 and 299 (Euclid’s division algorithm) HCF of 792 and 324 (Euclid’s division algorithm) HCF of 689 and 351 (Euclid’s division algorithm) HCF of 570 and 247 (Euclid’s division algorithm) HCF of 250 and 225 (Euclid’s division algorithm) HCF of 330 and 144 (Euclid’s division algorithm) HCF of 437 and 276 (Euclid’s division algorithm) HCF of 477 and 153 (Euclid’s division algorithm)
✅ Answer key — Euclid’s division algorithm
23 36 13 19 25 6 23 9 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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HCF × LCM = product Class 10 · Worksheet 4 · set 73
Name: Date: Score: / 6
Solve.
HCF of two numbers is 14 and their LCM is 336. One number is 42. Find the other. HCF of two numbers is 6 and their LCM is 36. One number is 12. Find the other. HCF of two numbers is 5 and their LCM is 30. One number is 15. Find the other. HCF of two numbers is 3 and their LCM is 126. One number is 21. Find the other. HCF of two numbers is 7 and their LCM is 294. One number is 42. Find the other. HCF of two numbers is 2 and their LCM is 42. One number is 14. Find the other.
✅ Answer key — HCF × LCM = product
112 18 10 18 49 6 TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Terminating decimals Class 10 · Worksheet 5 · set 73
Name: Date: Score: / 8
Answer without long division.
Does 27/50 have a terminating decimal expansion? Does 11/6 have a terminating decimal expansion? Does 119/500 have a terminating decimal expansion? Does 1364/1875 have a terminating decimal expansion? Does 129/80 have a terminating decimal expansion? Does 11/8 have a terminating decimal expansion? Does 573/400 have a terminating decimal expansion? Does 338/125 have a terminating decimal expansion?
✅ Answer key — Terminating decimals
Yes — terminating (denominator 2 × 5²) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2² × 5³) No — non-terminating repeating (denominator has the factor 3) Yes — terminating (denominator 2⁴ × 5) Yes — terminating (denominator 2³) Yes — terminating (denominator 2⁴ × 5²) Yes — terminating (denominator 5³) TalentJR · talentjr.in/real-numbers-class-10-worksheet
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Rational or irrational? Class 9–10 · Worksheet 6 · set 73
Name: Date: Score: / 12
Write rational or irrational.
Rational or irrational: √7 Rational or irrational: 9 + √24 Rational or irrational: 9√97 Rational or irrational: √100 Rational or irrational: √43 Rational or irrational: 6 + √19 Rational or irrational: 5 + √20 Rational or irrational: √11 Rational or irrational: 9√60 Rational or irrational: 8 + √86 Rational or irrational: 8√8 Rational or irrational: √58
✅ 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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